wepy.resampling.resamplers.wexplore module

exception wepy.resampling.resamplers.wexplore.RegionTreeError

Bases: Exception

Errors related to violations of constraints in RegionTree algorithms.

args

with_traceback()

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

wepy.resampling.resamplers.wexplore.calc_squashable_walkers_single_method(walker_weights, max_weight)

Calculate the maximum number of squashable walkers in collection of walkers, that still satisfies the max weight constraint.

We don’t guarantee or know if this is a completely optimal solver for this problem but it is assumed to be good enough in practice and no harm comes from underestimating it only a reduced potential performance.

Parameters:

• walker_weights (list of float) – The weights of the walkers

• max_weight (float) – The maximum weight a walker can have.

Returns:

n_squashable – The maximum number of squashable walkers.

Return type:

int

wepy.resampling.resamplers.wexplore.decide_merge_groups_single_method(walker_weights, balance, max_weight)

Use the ‘single’ method for determining the merge groups.

Determine a solution to the backpack-like problem of assigning squashed walkers to KEEP_MERGE walkers.

The single method just assigns all squashed walkers in the collection to a single walker, thus there is a single merge_group.

Parameters:

• walker_weights (list of float) – The weights of the walkers.

• balance (int) – The net change in the number of walkers we desire.

• max_weight (float) – The maximum weight a single walker can be.

Returns:

• merge_groups (list of list of int) – The merge group solution.

• result (bool) – Whether the merge group exceeds the max weight.

wepy.resampling.resamplers.wexplore.calc_max_num_clones(walker_weight, min_weight, max_num_walkers)

Parameters:

• walker_weight

• min_weight

• max_num_walkers

class wepy.resampling.resamplers.wexplore.RegionTree(init_state, max_n_regions=None, max_region_sizes=None, distance=None, pmin=None, pmax=None, merge_method='single')

Bases: DiGraph

Used internally in the WExploreResampler module. Not really intended to be used outside this module.

Initialize a graph with edges, name, or graph attributes.

Parameters:

• incoming_graph_data (input graph (optional, default: None)) – Data to initialize graph. If None (default) an empty graph is created. The data can be an edge list, or any NetworkX graph object. If the corresponding optional Python packages are installed the data can also be a 2D NumPy array, a SciPy sparse array, or a PyGraphviz graph.

• attr (keyword arguments, optional (default= no attributes)) – Attributes to add to graph as key=value pairs.

See also

convert

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G = nx.Graph(name="my graph")
>>> e = [(1, 2), (2, 3), (3, 4)]  # list of edges
>>> G = nx.Graph(e)

Arbitrary graph attribute pairs (key=value) may be assigned

>>> G = nx.Graph(e, day="Friday")
>>> G.graph
{'day': 'Friday'}

MERGE_METHODS = ('single',)

ROOT_NODE = ()

property merge_method

property distance

property images

property max_n_regions

property n_levels

property max_region_sizes

property pmin

property pmax

property walker_assignments

property walker_weights

property regions

add_child(parent_id, image_idx)

Parameters:

• parent_id

• image_idx

children(parent_id)

Parameters:

parent_id

level_nodes(level)

Get the nodes/regions at the specified level.

Parameters:

level

leaf_nodes()

branch_tree(parent_id, image)

Parameters:

• parent_id

• image

property max_num_walkers

property min_num_walkers

assign(state)

Parameters:

state

clear_walkers()

Remove all walkers from the regions.

place_walkers(walkers)

Parameters:

walkers

classmethod _max_n_merges(pmax, root, weights)

Parameters:

• pmax

• root

• weights

_calc_squashable_walkers(walker_weights)

Parameters:

walker_weights

_calc_max_num_clones(walker_weight)

Parameters:

walker_weight

_propagate_and_balance_shares(parental_balance, children_node_ids)

Parameters:

• parental_balance

• children_node_ids

_dispense_parental_shares(parental_balance, children_shares, children_donatable_shares, children_receivable_shares)

Given a parental balance and a set of children nodes, we dispense the shares indicated by the balance to the children nodes in a VALID but not necessarily optimal or desirable way. This merely checks for the hard constraints on the number of shares a region can either give or receive based on their capacity to clone and merge walkers.

An additional balancing step can be performed to redistribute them.

Parameters:

• parental_balance

• children_shares

• children_donatable_shares

• children_receivable_shares

_dispense_debit_shares(parental_balance, children_shares, children_donatable_shares)

For a negative parental balance we dispense it to the children nodes

Parameters:

• parental_balance

• children_shares

• children_donatable_shares

_dispense_credit_shares(parental_balance, children_shares, children_receivable_shares)

Parameters:

• parental_balance

• children_shares

• children_receivable_shares

_balance_children_shares(children_shares, children_donatable_shares, children_receivable_shares)

Given a dictionary mapping the child node_ids to the total number of shares they currently hold we balance between them in order to get an even distribution of the shares as possible.

Parameters:

• children_shares

• children_donatable_shares

• children_receivable_shares

_gen_best_donation(children_shares, children_donatable_shares, children_receivable_shares)

Given a the children shares generate the best donation. Returns the donor_node_id the acceptor_node_id and the donation that should be done between them and that will be guaranteed to be valid. (this is done by checking the attributes of the regions node however, no changes to node state are performed)

returns donor_node_id, acceptor_node_id, donation_amount

Parameters:

• children_shares

• children_donatable_shares

• children_receivable_shares

_find_best_donation_pair(children_donatable_shares, children_receivable_shares)

This method just returns which children have the most and least number of ‘shares’ which are the effective number of walker slots it will be granted in the next segment of dynamics in the simulation. This is essentially the amount of sampling effort that will be allocated to this region.

This method is give the dictionary of the childrens

Parameters:

• children_donatable_shares

• children_receivable_shares

_calc_share_donation(donor_n_shares, acceptor_n_shares, donor_donatable_shares, acceptor_receivable_shares)

Parameters:

• donor_n_shares

• acceptor_n_shares

• donor_donatable_shares

• acceptor_receivable_shares

_decide_merge_leaf(leaf, merge_groups)

Parameters:

• leaf

• merge_groups

_solve_merge_groupings(walker_weights, balance)

Parameters:

• walker_weights

• balance

_decide_clone_leaf(leaf, merge_groups, walkers_num_clones)

Parameters:

• leaf

• merge_groups

• walkers_num_clones

_decide_settle_balance()

Given the balances of all the leaves figure out actually how to settle all the balances. Returns the merge_groups and walkers_num_clones

_check_clone_merge_specs(merge_groups, walkers_num_clones)

This will perform the computations to get the weights of the clones and merges but does not actually assign them to slots. This is mainly for checking that we have not violated any rules.

Parameters:

• merge_groups

• walkers_num_clones

balance_tree(delta_walkers=0)

Do balancing between the branches of the tree. the delta_walkers kwarg can be used to increase or decrease the total number of walkers, but defaults to zero which will cause no net change in the number of walkers.

Parameters:

delta_walkers – (Default value = 0)

_adj

Data Descriptor class that syncs and resets cached properties adj and succ

The cached properties adj and succ are reset whenever _adj or _succ are set to new objects. In addition, the attributes _succ and _adj are synced so these two names point to the same object.

This object sits on a class and ensures that any instance of that class clears its cached properties “succ” and “adj” whenever the underlying instance attributes “_succ” or “_adj” are set to a new object. It only affects the set process of the obj._adj and obj._succ attribute. All get/del operations act as they normally would.

For info on Data Descriptors see: https://docs.python.org/3/howto/descriptor.html

_node

Data Descriptor class for _node that resets nodes cached_property when needed

This assumes that the cached_property G.node should be reset whenever G._node is set to a new value.

This object sits on a class and ensures that any instance of that class clears its cached property “nodes” whenever the underlying instance attribute “_node” is set to a new object. It only affects the set process of the obj._adj attribute. All get/del operations act as they normally would.

For info on Data Descriptors see: https://docs.python.org/3/howto/descriptor.html

_pred

Data Descriptor class for _pred that resets pred cached_property when needed

This assumes that the cached_property G.pred should be reset whenever G._pred is set to a new value.

This object sits on a class and ensures that any instance of that class clears its cached property “pred” whenever the underlying instance attribute “_pred” is set to a new object. It only affects the set process of the obj._pred attribute. All get/del operations act as they normally would.

For info on Data Descriptors see: https://docs.python.org/3/howto/descriptor.html

_succ

Data Descriptor class that syncs and resets cached properties adj and succ

The cached properties adj and succ are reset whenever _adj or _succ are set to new objects. In addition, the attributes _succ and _adj are synced so these two names point to the same object.

This object sits on a class and ensures that any instance of that class clears its cached properties “succ” and “adj” whenever the underlying instance attributes “_succ” or “_adj” are set to a new object. It only affects the set process of the obj._adj and obj._succ attribute. All get/del operations act as they normally would.

For info on Data Descriptors see: https://docs.python.org/3/howto/descriptor.html

add_edge(u_of_edge, v_of_edge, **attr)

Add an edge between u and v.

The nodes u and v will be automatically added if they are not already in the graph.

Edge attributes can be specified with keywords or by directly accessing the edge’s attribute dictionary. See examples below.

Parameters:

• u_of_edge (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.

• v_of_edge (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.

• attr (keyword arguments, optional) – Edge data (or labels or objects) can be assigned using keyword arguments.

See also

add_edges_from

add a collection of edges

Notes

Adding an edge that already exists updates the edge data.

Many NetworkX algorithms designed for weighted graphs use an edge attribute (by default weight) to hold a numerical value.

Examples

The following all add the edge e=(1, 2) to graph G:

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> e = (1, 2)
>>> G.add_edge(1, 2)  # explicit two-node form
>>> G.add_edge(*e)  # single edge as tuple of two nodes
>>> G.add_edges_from([(1, 2)])  # add edges from iterable container

Associate data to edges using keywords:

>>> G.add_edge(1, 2, weight=3)
>>> G.add_edge(1, 3, weight=7, capacity=15, length=342.7)

For non-string attribute keys, use subscript notation.

>>> G.add_edge(1, 2)
>>> G[1][2].update({0: 5})
>>> G.edges[1, 2].update({0: 5})

add_edges_from(ebunch_to_add, **attr)

Add all the edges in ebunch_to_add.

Parameters:

• ebunch_to_add (container of edges) – Each edge given in the container will be added to the graph. The edges must be given as 2-tuples (u, v) or 3-tuples (u, v, d) where d is a dictionary containing edge data.

• attr (keyword arguments, optional) – Edge data (or labels or objects) can be assigned using keyword arguments.

See also

add_edge

add a single edge

add_weighted_edges_from

convenient way to add weighted edges

Notes

Adding the same edge twice has no effect but any edge data will be updated when each duplicate edge is added.

Edge attributes specified in an ebunch take precedence over attributes specified via keyword arguments.

When adding edges from an iterator over the graph you are changing, a RuntimeError can be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_edges), and pass this object to G.add_edges_from.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edges_from([(0, 1), (1, 2)])  # using a list of edge tuples
>>> e = zip(range(0, 3), range(1, 4))
>>> G.add_edges_from(e)  # Add the path graph 0-1-2-3

Associate data to edges

>>> G.add_edges_from([(1, 2), (2, 3)], weight=3)
>>> G.add_edges_from([(3, 4), (1, 4)], label="WN2898")

Evaluate an iterator over a graph if using it to modify the same graph

>>> G = nx.DiGraph([(1, 2), (2, 3), (3, 4)])
>>> # Grow graph by one new node, adding edges to all existing nodes.
>>> # wrong way - will raise RuntimeError
>>> # G.add_edges_from(((5, n) for n in G.nodes))
>>> # right way - note that there will be no self-edge for node 5
>>> G.add_edges_from(list((5, n) for n in G.nodes))

add_node(node_for_adding, **attr)

Add a single node node_for_adding and update node attributes.

Parameters:

• node_for_adding (node) – A node can be any hashable Python object except None.

• attr (keyword arguments, optional) – Set or change node attributes using key=value.

See also

add_nodes_from

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_node(1)
>>> G.add_node("Hello")
>>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)])
>>> G.add_node(K3)
>>> G.number_of_nodes()
3

Use keywords set/change node attributes:

>>> G.add_node(1, size=10)
>>> G.add_node(3, weight=0.4, UTM=("13S", 382871, 3972649))

Notes

A hashable object is one that can be used as a key in a Python dictionary. This includes strings, numbers, tuples of strings and numbers, etc.

On many platforms hashable items also include mutables such as NetworkX Graphs, though one should be careful that the hash doesn’t change on mutables.

add_nodes_from(nodes_for_adding, **attr)

Add multiple nodes.

Parameters:

• nodes_for_adding (iterable container) – A container of nodes (list, dict, set, etc.). OR A container of (node, attribute dict) tuples. Node attributes are updated using the attribute dict.

• attr (keyword arguments, optional (default= no attributes)) – Update attributes for all nodes in nodes. Node attributes specified in nodes as a tuple take precedence over attributes specified via keyword arguments.

See also

add_node

Notes

When adding nodes from an iterator over the graph you are changing, a RuntimeError can be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_nodes), and pass this object to G.add_nodes_from.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_nodes_from("Hello")
>>> K3 = nx.Graph([(0, 1), (1, 2), (2, 0)])
>>> G.add_nodes_from(K3)
>>> sorted(G.nodes(), key=str)
[0, 1, 2, 'H', 'e', 'l', 'o']

Use keywords to update specific node attributes for every node.

>>> G.add_nodes_from([1, 2], size=10)
>>> G.add_nodes_from([3, 4], weight=0.4)

Use (node, attrdict) tuples to update attributes for specific nodes.

>>> G.add_nodes_from([(1, dict(size=11)), (2, {"color": "blue"})])
>>> G.nodes[1]["size"]
11
>>> H = nx.Graph()
>>> H.add_nodes_from(G.nodes(data=True))
>>> H.nodes[1]["size"]
11

Evaluate an iterator over a graph if using it to modify the same graph

>>> G = nx.DiGraph([(0, 1), (1, 2), (3, 4)])
>>> # wrong way - will raise RuntimeError
>>> # G.add_nodes_from(n + 1 for n in G.nodes)
>>> # correct way
>>> G.add_nodes_from(list(n + 1 for n in G.nodes))

add_weighted_edges_from(ebunch_to_add, weight='weight', **attr)

Add weighted edges in ebunch_to_add with specified weight attr

Parameters:

• ebunch_to_add (container of edges) – Each edge given in the list or container will be added to the graph. The edges must be given as 3-tuples (u, v, w) where w is a number.

• weight (string, optional (default= 'weight')) – The attribute name for the edge weights to be added.

• attr (keyword arguments, optional (default= no attributes)) – Edge attributes to add/update for all edges.

See also

add_edge

add a single edge

add_edges_from

add multiple edges

Notes

Adding the same edge twice for Graph/DiGraph simply updates the edge data. For MultiGraph/MultiDiGraph, duplicate edges are stored.

When adding edges from an iterator over the graph you are changing, a RuntimeError can be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_edges), and pass this object to G.add_weighted_edges_from.

Examples

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_weighted_edges_from([(0, 1, 3.0), (1, 2, 7.5)])

Evaluate an iterator over edges before passing it

>>> G = nx.Graph([(1, 2), (2, 3), (3, 4)])
>>> weight = 0.1
>>> # Grow graph by one new node, adding edges to all existing nodes.
>>> # wrong way - will raise RuntimeError
>>> # G.add_weighted_edges_from(((5, n, weight) for n in G.nodes))
>>> # correct way - note that there will be no self-edge for node 5
>>> G.add_weighted_edges_from(list((5, n, weight) for n in G.nodes))

property adj

Graph adjacency object holding the neighbors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edge-data-dict. So G.adj[3][2][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.adj behaves like a dict. Useful idioms include for nbr, datadict in G.adj[n].items():.

The neighbor information is also provided by subscripting the graph. So for nbr, foovalue in G[node].data(‘foo’, default=1): works.

For directed graphs, G.adj holds outgoing (successor) info.

adjacency()

Returns an iterator over (node, adjacency dict) tuples for all nodes.

For directed graphs, only outgoing neighbors/adjacencies are included.

Returns:

adj_iter – An iterator over (node, adjacency dictionary) for all nodes in the graph.

Return type:

iterator

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> [(n, nbrdict) for n, nbrdict in G.adjacency()]
[(0, {1: {}}), (1, {0: {}, 2: {}}), (2, {1: {}, 3: {}}), (3, {2: {}})]

adjlist_inner_dict_factory

alias of dict

adjlist_outer_dict_factory

alias of dict

clear()

Remove all nodes and edges from the graph.

This also removes the name, and all graph, node, and edge attributes.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.clear()
>>> list(G.nodes)
[]
>>> list(G.edges)
[]

clear_edges()

Remove all edges from the graph without altering nodes.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.clear_edges()
>>> list(G.nodes)
[0, 1, 2, 3]
>>> list(G.edges)
[]

copy(as_view=False)

Returns a copy of the graph.

The copy method by default returns an independent shallow copy of the graph and attributes. That is, if an attribute is a container, that container is shared by the original an the copy. Use Python’s copy.deepcopy for new containers.

If as_view is True then a view is returned instead of a copy.

Notes

All copies reproduce the graph structure, but data attributes may be handled in different ways. There are four types of copies of a graph that people might want.

Deepcopy – A “deepcopy” copies the graph structure as well as all data attributes and any objects they might contain. The entire graph object is new so that changes in the copy do not affect the original object. (see Python’s copy.deepcopy)

Data Reference (Shallow) – For a shallow copy the graph structure is copied but the edge, node and graph attribute dicts are references to those in the original graph. This saves time and memory but could cause confusion if you change an attribute in one graph and it changes the attribute in the other. NetworkX does not provide this level of shallow copy.

Independent Shallow – This copy creates new independent attribute dicts and then does a shallow copy of the attributes. That is, any attributes that are containers are shared between the new graph and the original. This is exactly what dict.copy() provides. You can obtain this style copy using:

>>> G = nx.path_graph(5)
>>> H = G.copy()
>>> H = G.copy(as_view=False)
>>> H = nx.Graph(G)
>>> H = G.__class__(G)

Fresh Data – For fresh data, the graph structure is copied while new empty data attribute dicts are created. The resulting graph is independent of the original and it has no edge, node or graph attributes. Fresh copies are not enabled. Instead use:

>>> H = G.__class__()
>>> H.add_nodes_from(G)
>>> H.add_edges_from(G.edges)

View – Inspired by dict-views, graph-views act like read-only versions of the original graph, providing a copy of the original structure without requiring any memory for copying the information.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Parameters:

as_view (bool, optional (default=False)) – If True, the returned graph-view provides a read-only view of the original graph without actually copying any data.

Returns:

G – A copy of the graph.

Return type:

Graph

See also

to_directed

return a directed copy of the graph.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> H = G.copy()

property degree

A DegreeView for the Graph as G.degree or G.degree().

The node degree is the number of edges adjacent to the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iterator for (node, degree) as well as lookup for the degree for a single node.

Parameters:

• nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

• weight (string or None, optional (default=None)) – The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

Returns:

If multiple nodes are requested (the default), returns a DiDegreeView mapping nodes to their degree. If a single node is requested, returns the degree of the node as an integer.

Return type:

DiDegreeView or int

See also

in_degree, out_degree

Examples

>>> G = nx.DiGraph()  # or MultiDiGraph
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.degree(0)  # node 0 with degree 1
1
>>> list(G.degree([0, 1, 2]))
[(0, 1), (1, 2), (2, 2)]

edge_attr_dict_factory

alias of dict

edge_subgraph(edges)

Returns the subgraph induced by the specified edges.

The induced subgraph contains each edge in edges and each node incident to any one of those edges.

Parameters:

edges (iterable) – An iterable of edges in this graph.

Returns:

G – An edge-induced subgraph of this graph with the same edge attributes.

Return type:

Graph

Notes

The graph, edge, and node attributes in the returned subgraph view are references to the corresponding attributes in the original graph. The view is read-only.

To create a full graph version of the subgraph with its own copy of the edge or node attributes, use:

G.edge_subgraph(edges).copy()

Examples

>>> G = nx.path_graph(5)
>>> H = G.edge_subgraph([(0, 1), (3, 4)])
>>> list(H.nodes)
[0, 1, 3, 4]
>>> list(H.edges)
[(0, 1), (3, 4)]

property edges

An OutEdgeView of the DiGraph as G.edges or G.edges().

edges(self, nbunch=None, data=False, default=None)

The OutEdgeView provides set-like operations on the edge-tuples as well as edge attribute lookup. When called, it also provides an EdgeDataView object which allows control of access to edge attributes (but does not provide set-like operations). Hence, G.edges[u, v][‘color’] provides the value of the color attribute for edge (u, v) while for (u, v, c) in G.edges.data(‘color’, default=’red’): iterates through all the edges yielding the color attribute with default ‘red’ if no color attribute exists.

Parameters:

• nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges from these nodes.

• data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).

• default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns:

edges – A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as edges[u, v][‘foo’].

Return type:

OutEdgeView

See also

in_edges, out_edges

Notes

Nodes in nbunch that are not in the graph will be (quietly) ignored. For directed graphs this returns the out-edges.

Examples

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> nx.add_path(G, [0, 1, 2])
>>> G.add_edge(2, 3, weight=5)
>>> [e for e in G.edges]
[(0, 1), (1, 2), (2, 3)]
>>> G.edges.data()  # default data is {} (empty dict)
OutEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
>>> G.edges.data("weight", default=1)
OutEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
>>> G.edges([0, 2])  # only edges originating from these nodes
OutEdgeDataView([(0, 1), (2, 3)])
>>> G.edges(0)  # only edges from node 0
OutEdgeDataView([(0, 1)])

get_edge_data(u, v, default=None)

Returns the attribute dictionary associated with edge (u, v).

This is identical to G[u][v] except the default is returned instead of an exception if the edge doesn’t exist.

Parameters:

• u (nodes)

• v (nodes)

• default (any Python object (default=None)) – Value to return if the edge (u, v) is not found.

Returns:

edge_dict – The edge attribute dictionary.

Return type:

dictionary

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G[0][1]
{}

Warning: Assigning to G[u][v] is not permitted. But it is safe to assign attributes G[u][v][‘foo’]

>>> G[0][1]["weight"] = 7
>>> G[0][1]["weight"]
7
>>> G[1][0]["weight"]
7

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.get_edge_data(0, 1)  # default edge data is {}
{}
>>> e = (0, 1)
>>> G.get_edge_data(*e)  # tuple form
{}
>>> G.get_edge_data("a", "b", default=0)  # edge not in graph, return 0
0

graph_attr_dict_factory

alias of dict

has_edge(u, v)

Returns True if the edge (u, v) is in the graph.

This is the same as v in G[u] without KeyError exceptions.

Parameters:

• u (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.

• v (nodes) – Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects.

Returns:

edge_ind – True if edge is in the graph, False otherwise.

Return type:

bool

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.has_edge(0, 1)  # using two nodes
True
>>> e = (0, 1)
>>> G.has_edge(*e)  #  e is a 2-tuple (u, v)
True
>>> e = (0, 1, {"weight": 7})
>>> G.has_edge(*e[:2])  # e is a 3-tuple (u, v, data_dictionary)
True

The following syntax are equivalent:

>>> G.has_edge(0, 1)
True
>>> 1 in G[0]  # though this gives KeyError if 0 not in G
True

has_node(n)

Returns True if the graph contains the node n.

Identical to n in G

Parameters:

n (node)

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.has_node(0)
True

It is more readable and simpler to use

>>> 0 in G
True

has_predecessor(u, v)

Returns True if node u has predecessor v.

This is true if graph has the edge u<-v.

has_successor(u, v)

Returns True if node u has successor v.

This is true if graph has the edge u->v.

property in_degree

An InDegreeView for (node, in_degree) or in_degree for single node.

The node in_degree is the number of edges pointing to the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iteration over (node, in_degree) as well as lookup for the degree for a single node.

Parameters:

• nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

• weight (string or None, optional (default=None)) – The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

Returns:

• If a single node is requested

• deg (int) – In-degree of the node

• OR if multiple nodes are requested

• nd_iter (iterator) – The iterator returns two-tuples of (node, in-degree).

See also

degree, out_degree

Examples

>>> G = nx.DiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.in_degree(0)  # node 0 with degree 0
0
>>> list(G.in_degree([0, 1, 2]))
[(0, 0), (1, 1), (2, 1)]

property in_edges

A view of the in edges of the graph as G.in_edges or G.in_edges().

in_edges(self, nbunch=None, data=False, default=None):

Parameters:

• nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

• data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).

• default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns:

in_edges – A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as edges[u, v][‘foo’].

Return type:

InEdgeView or InEdgeDataView

Examples

>>> G = nx.DiGraph()
>>> G.add_edge(1, 2, color="blue")
>>> G.in_edges()
InEdgeView([(1, 2)])
>>> G.in_edges(nbunch=2)
InEdgeDataView([(1, 2)])

See also

edges

is_directed()

Returns True if graph is directed, False otherwise.

is_multigraph()

Returns True if graph is a multigraph, False otherwise.

property name

String identifier of the graph.

This graph attribute appears in the attribute dict G.graph keyed by the string “name”. as well as an attribute (technically a property) G.name. This is entirely user controlled.

nbunch_iter(nbunch=None)

Returns an iterator over nodes contained in nbunch that are also in the graph.

The nodes in nbunch are checked for membership in the graph and if not are silently ignored.

Parameters:

nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

Returns:

niter – An iterator over nodes in nbunch that are also in the graph. If nbunch is None, iterate over all nodes in the graph.

Return type:

iterator

Raises:

NetworkXError – If nbunch is not a node or sequence of nodes. If a node in nbunch is not hashable.

See also

Graph.__iter__

Notes

When nbunch is an iterator, the returned iterator yields values directly from nbunch, becoming exhausted when nbunch is exhausted.

To test whether nbunch is a single node, one can use “if nbunch in self:”, even after processing with this routine.

If nbunch is not a node or a (possibly empty) sequence/iterator or None, a NetworkXError is raised. Also, if any object in nbunch is not hashable, a NetworkXError is raised.

neighbors(n)

Returns an iterator over successor nodes of n.

A successor of n is a node m such that there exists a directed edge from n to m.

Parameters:

n (node) – A node in the graph

Raises:

NetworkXError – If n is not in the graph.

See also

predecessors

Notes

neighbors() and successors() are the same.

node_attr_dict_factory

alias of dict

node_dict_factory

alias of dict

property nodes

A NodeView of the Graph as G.nodes or G.nodes().

Can be used as G.nodes for data lookup and for set-like operations. Can also be used as G.nodes(data=’color’, default=None) to return a NodeDataView which reports specific node data but no set operations. It presents a dict-like interface as well with G.nodes.items() iterating over (node, nodedata) 2-tuples and G.nodes[3][‘foo’] providing the value of the foo attribute for node 3. In addition, a view G.nodes.data(‘foo’) provides a dict-like interface to the foo attribute of each node. G.nodes.data(‘foo’, default=1) provides a default for nodes that do not have attribute foo.

Parameters:

• data (string or bool, optional (default=False)) – The node attribute returned in 2-tuple (n, ddict[data]). If True, return entire node attribute dict as (n, ddict). If False, return just the nodes n.

• default (value, optional (default=None)) – Value used for nodes that don’t have the requested attribute. Only relevant if data is not True or False.

Returns:

Allows set-like operations over the nodes as well as node attribute dict lookup and calling to get a NodeDataView. A NodeDataView iterates over (n, data) and has no set operations. A NodeView iterates over n and includes set operations.

When called, if data is False, an iterator over nodes. Otherwise an iterator of 2-tuples (node, attribute value) where the attribute is specified in data. If data is True then the attribute becomes the entire data dictionary.

Return type:

NodeView

Notes

If your node data is not needed, it is simpler and equivalent to use the expression for n in G, or list(G).

Examples

There are two simple ways of getting a list of all nodes in the graph:

>>> G = nx.path_graph(3)
>>> list(G.nodes)
[0, 1, 2]
>>> list(G)
[0, 1, 2]

To get the node data along with the nodes:

>>> G.add_node(1, time="5pm")
>>> G.nodes[0]["foo"] = "bar"
>>> list(G.nodes(data=True))
[(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]
>>> list(G.nodes.data())
[(0, {'foo': 'bar'}), (1, {'time': '5pm'}), (2, {})]

>>> list(G.nodes(data="foo"))
[(0, 'bar'), (1, None), (2, None)]
>>> list(G.nodes.data("foo"))
[(0, 'bar'), (1, None), (2, None)]

>>> list(G.nodes(data="time"))
[(0, None), (1, '5pm'), (2, None)]
>>> list(G.nodes.data("time"))
[(0, None), (1, '5pm'), (2, None)]

>>> list(G.nodes(data="time", default="Not Available"))
[(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]
>>> list(G.nodes.data("time", default="Not Available"))
[(0, 'Not Available'), (1, '5pm'), (2, 'Not Available')]

If some of your nodes have an attribute and the rest are assumed to have a default attribute value you can create a dictionary from node/attribute pairs using the default keyword argument to guarantee the value is never None:

>>> G = nx.Graph()
>>> G.add_node(0)
>>> G.add_node(1, weight=2)
>>> G.add_node(2, weight=3)
>>> dict(G.nodes(data="weight", default=1))
{0: 1, 1: 2, 2: 3}

number_of_edges(u=None, v=None)

Returns the number of edges between two nodes.

Parameters:

• u (nodes, optional (default=all edges)) – If u and v are specified, return the number of edges between u and v. Otherwise return the total number of all edges.

• v (nodes, optional (default=all edges)) – If u and v are specified, return the number of edges between u and v. Otherwise return the total number of all edges.

Returns:

nedges – The number of edges in the graph. If nodes u and v are specified return the number of edges between those nodes. If the graph is directed, this only returns the number of edges from u to v.

Return type:

int

See also

size

Examples

For undirected graphs, this method counts the total number of edges in the graph:

>>> G = nx.path_graph(4)
>>> G.number_of_edges()
3

If you specify two nodes, this counts the total number of edges joining the two nodes:

>>> G.number_of_edges(0, 1)
1

For directed graphs, this method can count the total number of directed edges from u to v:

>>> G = nx.DiGraph()
>>> G.add_edge(0, 1)
>>> G.add_edge(1, 0)
>>> G.number_of_edges(0, 1)
1

number_of_nodes()

Returns the number of nodes in the graph.

Returns:

nnodes – The number of nodes in the graph.

Return type:

int

See also

order

identical method

__len__

identical method

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.number_of_nodes()
3

order()

Returns the number of nodes in the graph.

Returns:

nnodes – The number of nodes in the graph.

Return type:

int

See also

number_of_nodes

identical method

__len__

identical method

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.order()
3

property out_degree

An OutDegreeView for (node, out_degree)

The node out_degree is the number of edges pointing out of the node. The weighted node degree is the sum of the edge weights for edges incident to that node.

This object provides an iterator over (node, out_degree) as well as lookup for the degree for a single node.

Parameters:

• nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges incident to these nodes.

• weight (string or None, optional (default=None)) – The name of an edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1. The degree is the sum of the edge weights adjacent to the node.

Returns:

• If a single node is requested

• deg (int) – Out-degree of the node

• OR if multiple nodes are requested

• nd_iter (iterator) – The iterator returns two-tuples of (node, out-degree).

See also

degree, in_degree

Examples

>>> G = nx.DiGraph()
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.out_degree(0)  # node 0 with degree 1
1
>>> list(G.out_degree([0, 1, 2]))
[(0, 1), (1, 1), (2, 1)]

property out_edges

An OutEdgeView of the DiGraph as G.edges or G.edges().

edges(self, nbunch=None, data=False, default=None)

The OutEdgeView provides set-like operations on the edge-tuples as well as edge attribute lookup. When called, it also provides an EdgeDataView object which allows control of access to edge attributes (but does not provide set-like operations). Hence, G.edges[u, v][‘color’] provides the value of the color attribute for edge (u, v) while for (u, v, c) in G.edges.data(‘color’, default=’red’): iterates through all the edges yielding the color attribute with default ‘red’ if no color attribute exists.

Parameters:

• nbunch (single node, container, or all nodes (default= all nodes)) – The view will only report edges from these nodes.

• data (string or bool, optional (default=False)) – The edge attribute returned in 3-tuple (u, v, ddict[data]). If True, return edge attribute dict in 3-tuple (u, v, ddict). If False, return 2-tuple (u, v).

• default (value, optional (default=None)) – Value used for edges that don’t have the requested attribute. Only relevant if data is not True or False.

Returns:

edges – A view of edge attributes, usually it iterates over (u, v) or (u, v, d) tuples of edges, but can also be used for attribute lookup as edges[u, v][‘foo’].

Return type:

OutEdgeView

See also

in_edges, out_edges

Notes

Nodes in nbunch that are not in the graph will be (quietly) ignored. For directed graphs this returns the out-edges.

Examples

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> nx.add_path(G, [0, 1, 2])
>>> G.add_edge(2, 3, weight=5)
>>> [e for e in G.edges]
[(0, 1), (1, 2), (2, 3)]
>>> G.edges.data()  # default data is {} (empty dict)
OutEdgeDataView([(0, 1, {}), (1, 2, {}), (2, 3, {'weight': 5})])
>>> G.edges.data("weight", default=1)
OutEdgeDataView([(0, 1, 1), (1, 2, 1), (2, 3, 5)])
>>> G.edges([0, 2])  # only edges originating from these nodes
OutEdgeDataView([(0, 1), (2, 3)])
>>> G.edges(0)  # only edges from node 0
OutEdgeDataView([(0, 1)])

property pred

Graph adjacency object holding the predecessors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edge-data-dict. So G.pred[2][3][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.pred behaves like a dict. Useful idioms include for nbr, datadict in G.pred[n].items():. A data-view not provided by dicts also exists: for nbr, foovalue in G.pred[node].data(‘foo’): A default can be set via a default argument to the data method.

predecessors(n)

Returns an iterator over predecessor nodes of n.

A predecessor of n is a node m such that there exists a directed edge from m to n.

Parameters:

n (node) – A node in the graph

Raises:

NetworkXError – If n is not in the graph.

See also

successors

remove_edge(u, v)

Remove the edge between u and v.

Parameters:

• u (nodes) – Remove the edge between nodes u and v.

• v (nodes) – Remove the edge between nodes u and v.

Raises:

NetworkXError – If there is not an edge between u and v.

See also

remove_edges_from

remove a collection of edges

Examples

>>> G = nx.Graph()  # or DiGraph, etc
>>> nx.add_path(G, [0, 1, 2, 3])
>>> G.remove_edge(0, 1)
>>> e = (1, 2)
>>> G.remove_edge(*e)  # unpacks e from an edge tuple
>>> e = (2, 3, {"weight": 7})  # an edge with attribute data
>>> G.remove_edge(*e[:2])  # select first part of edge tuple

remove_edges_from(ebunch)

Remove all edges specified in ebunch.

Parameters:

ebunch (list or container of edge tuples) –

Each edge given in the list or container will be removed from the graph. The edges can be:

• 2-tuples (u, v) edge between u and v.

• 3-tuples (u, v, k) where k is ignored.

See also

remove_edge

remove a single edge

Notes

Will fail silently if an edge in ebunch is not in the graph.

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> ebunch = [(1, 2), (2, 3)]
>>> G.remove_edges_from(ebunch)

remove_node(n)

Remove node n.

Removes the node n and all adjacent edges. Attempting to remove a nonexistent node will raise an exception.

Parameters:

n (node) – A node in the graph

Raises:

NetworkXError – If n is not in the graph.

See also

remove_nodes_from

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> list(G.edges)
[(0, 1), (1, 2)]
>>> G.remove_node(1)
>>> list(G.edges)
[]

remove_nodes_from(nodes)

Remove multiple nodes.

Parameters:

nodes (iterable container) – A container of nodes (list, dict, set, etc.). If a node in the container is not in the graph it is silently ignored.

See also

remove_node

Notes

When removing nodes from an iterator over the graph you are changing, a RuntimeError will be raised with message: RuntimeError: dictionary changed size during iteration. This happens when the graph’s underlying dictionary is modified during iteration. To avoid this error, evaluate the iterator into a separate object, e.g. by using list(iterator_of_nodes), and pass this object to G.remove_nodes_from.

Examples

>>> G = nx.path_graph(3)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> e = list(G.nodes)
>>> e
[0, 1, 2]
>>> G.remove_nodes_from(e)
>>> list(G.nodes)
[]

Evaluate an iterator over a graph if using it to modify the same graph

>>> G = nx.DiGraph([(0, 1), (1, 2), (3, 4)])
>>> # this command will fail, as the graph's dict is modified during iteration
>>> # G.remove_nodes_from(n for n in G.nodes if n < 2)
>>> # this command will work, since the dictionary underlying graph is not modified
>>> G.remove_nodes_from(list(n for n in G.nodes if n < 2))

reverse(copy=True)

Returns the reverse of the graph.

The reverse is a graph with the same nodes and edges but with the directions of the edges reversed.

Parameters:

copy (bool optional (default=True)) – If True, return a new DiGraph holding the reversed edges. If False, the reverse graph is created using a view of the original graph.

size(weight=None)

Returns the number of edges or total of all edge weights.

Parameters:

weight (string or None, optional (default=None)) – The edge attribute that holds the numerical value used as a weight. If None, then each edge has weight 1.

Returns:

size – The number of edges or (if weight keyword is provided) the total weight sum.

If weight is None, returns an int. Otherwise a float (or more general numeric if the weights are more general).

Return type:

numeric

See also

number_of_edges

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.size()
3

>>> G = nx.Graph()  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> G.add_edge("a", "b", weight=2)
>>> G.add_edge("b", "c", weight=4)
>>> G.size()
2
>>> G.size(weight="weight")
6.0

subgraph(nodes)

Returns a SubGraph view of the subgraph induced on nodes.

The induced subgraph of the graph contains the nodes in nodes and the edges between those nodes.

Parameters:

nodes (list, iterable) – A container of nodes which will be iterated through once.

Returns:

G – A subgraph view of the graph. The graph structure cannot be changed but node/edge attributes can and are shared with the original graph.

Return type:

SubGraph View

Notes

The graph, edge and node attributes are shared with the original graph. Changes to the graph structure is ruled out by the view, but changes to attributes are reflected in the original graph.

To create a subgraph with its own copy of the edge/node attributes use: G.subgraph(nodes).copy()

For an inplace reduction of a graph to a subgraph you can remove nodes: G.remove_nodes_from([n for n in G if n not in set(nodes)])

Subgraph views are sometimes NOT what you want. In most cases where you want to do more than simply look at the induced edges, it makes more sense to just create the subgraph as its own graph with code like:

# Create a subgraph SG based on a (possibly multigraph) G
SG = G.__class__()
SG.add_nodes_from((n, G.nodes[n]) for n in largest_wcc)
if SG.is_multigraph():
    SG.add_edges_from(
        (n, nbr, key, d)
        for n, nbrs in G.adj.items()
        if n in largest_wcc
        for nbr, keydict in nbrs.items()
        if nbr in largest_wcc
        for key, d in keydict.items()
    )
else:
    SG.add_edges_from(
        (n, nbr, d)
        for n, nbrs in G.adj.items()
        if n in largest_wcc
        for nbr, d in nbrs.items()
        if nbr in largest_wcc
    )
SG.graph.update(G.graph)

Examples

>>> G = nx.path_graph(4)  # or DiGraph, MultiGraph, MultiDiGraph, etc
>>> H = G.subgraph([0, 1, 2])
>>> list(H.edges)
[(0, 1), (1, 2)]

property succ

Graph adjacency object holding the successors of each node.

This object is a read-only dict-like structure with node keys and neighbor-dict values. The neighbor-dict is keyed by neighbor to the edge-data-dict. So G.succ[3][2][‘color’] = ‘blue’ sets the color of the edge (3, 2) to “blue”.

Iterating over G.succ behaves like a dict. Useful idioms include for nbr, datadict in G.succ[n].items():. A data-view not provided by dicts also exists: for nbr, foovalue in G.succ[node].data(‘foo’): and a default can be set via a default argument to the data method.

The neighbor information is also provided by subscripting the graph. So for nbr, foovalue in G[node].data(‘foo’, default=1): works.

For directed graphs, G.adj is identical to G.succ.

successors(n)

Returns an iterator over successor nodes of n.

A successor of n is a node m such that there exists a directed edge from n to m.

Parameters:

n (node) – A node in the graph

Raises:

NetworkXError – If n is not in the graph.

See also

predecessors

Notes

neighbors() and successors() are the same.

to_directed(as_view=False)

Returns a directed representation of the graph.

Returns:

G – A directed graph with the same name, same nodes, and with each edge (u, v, data) replaced by two directed edges (u, v, data) and (v, u, data).

Return type:

DiGraph

Notes

This returns a “deepcopy” of the edge, node, and graph attributes which attempts to completely copy all of the data and references.

This is in contrast to the similar D=DiGraph(G) which returns a shallow copy of the data.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Warning: If you have subclassed Graph to use dict-like objects in the data structure, those changes do not transfer to the DiGraph created by this method.

Examples

>>> G = nx.Graph()  # or MultiGraph, etc
>>> G.add_edge(0, 1)
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1), (1, 0)]

If already directed, return a (deep) copy

>>> G = nx.DiGraph()  # or MultiDiGraph, etc
>>> G.add_edge(0, 1)
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1)]

to_directed_class()

Returns the class to use for empty directed copies.

If you subclass the base classes, use this to designate what directed class to use for to_directed() copies.

to_undirected(reciprocal=False, as_view=False)

Returns an undirected representation of the digraph.

Parameters:

• reciprocal (bool (optional)) – If True only keep edges that appear in both directions in the original digraph.

• as_view (bool (optional, default=False)) – If True return an undirected view of the original directed graph.

Returns:

G – An undirected graph with the same name and nodes and with edge (u, v, data) if either (u, v, data) or (v, u, data) is in the digraph. If both edges exist in digraph and their edge data is different, only one edge is created with an arbitrary choice of which edge data to use. You must check and correct for this manually if desired.

Return type:

Graph

See also

Graph, copy, add_edge, add_edges_from

Notes

If edges in both directions (u, v) and (v, u) exist in the graph, attributes for the new undirected edge will be a combination of the attributes of the directed edges. The edge data is updated in the (arbitrary) order that the edges are encountered. For more customized control of the edge attributes use add_edge().

This returns a “deepcopy” of the edge, node, and graph attributes which attempts to completely copy all of the data and references.

This is in contrast to the similar G=DiGraph(D) which returns a shallow copy of the data.

See the Python copy module for more information on shallow and deep copies, https://docs.python.org/3/library/copy.html.

Warning: If you have subclassed DiGraph to use dict-like objects in the data structure, those changes do not transfer to the Graph created by this method.

Examples

>>> G = nx.path_graph(2)  # or MultiGraph, etc
>>> H = G.to_directed()
>>> list(H.edges)
[(0, 1), (1, 0)]
>>> G2 = H.to_undirected()
>>> list(G2.edges)
[(0, 1)]

to_undirected_class()

Returns the class to use for empty undirected copies.

If you subclass the base classes, use this to designate what directed class to use for to_directed() copies.

update(edges=None, nodes=None)

Update the graph using nodes/edges/graphs as input.

Like dict.update, this method takes a graph as input, adding the graph’s nodes and edges to this graph. It can also take two inputs: edges and nodes. Finally it can take either edges or nodes. To specify only nodes the keyword nodes must be used.

The collections of edges and nodes are treated similarly to the add_edges_from/add_nodes_from methods. When iterated, they should yield 2-tuples (u, v) or 3-tuples (u, v, datadict).

Parameters:

• edges (Graph object, collection of edges, or None) – The first parameter can be a graph or some edges. If it has attributes nodes and edges, then it is taken to be a Graph-like object and those attributes are used as collections of nodes and edges to be added to the graph. If the first parameter does not have those attributes, it is treated as a collection of edges and added to the graph. If the first argument is None, no edges are added.

• nodes (collection of nodes, or None) – The second parameter is treated as a collection of nodes to be added to the graph unless it is None. If edges is None and nodes is None an exception is raised. If the first parameter is a Graph, then nodes is ignored.

Examples

>>> G = nx.path_graph(5)
>>> G.update(nx.complete_graph(range(4, 10)))
>>> from itertools import combinations
>>> edges = (
...     (u, v, {"power": u * v})
...     for u, v in combinations(range(10, 20), 2)
...     if u * v < 225
... )
>>> nodes = [1000]  # for singleton, use a container
>>> G.update(edges, nodes)

Notes

It you want to update the graph using an adjacency structure it is straightforward to obtain the edges/nodes from adjacency. The following examples provide common cases, your adjacency may be slightly different and require tweaks of these examples:

>>> # dict-of-set/list/tuple
>>> adj = {1: {2, 3}, 2: {1, 3}, 3: {1, 2}}
>>> e = [(u, v) for u, nbrs in adj.items() for v in nbrs]
>>> G.update(edges=e, nodes=adj)

>>> DG = nx.DiGraph()
>>> # dict-of-dict-of-attribute
>>> adj = {1: {2: 1.3, 3: 0.7}, 2: {1: 1.4}, 3: {1: 0.7}}
>>> e = [(u, v, {"weight": d}) for u, nbrs in adj.items() for v, d in nbrs.items()]
>>> DG.update(edges=e, nodes=adj)

>>> # dict-of-dict-of-dict
>>> adj = {1: {2: {"weight": 1.3}, 3: {"color": 0.7, "weight": 1.2}}}
>>> e = [(u, v, {"weight": d}) for u, nbrs in adj.items() for v, d in nbrs.items()]
>>> DG.update(edges=e, nodes=adj)

>>> # predecessor adjacency (dict-of-set)
>>> pred = {1: {2, 3}, 2: {3}, 3: {3}}
>>> e = [(v, u) for u, nbrs in pred.items() for v in nbrs]

>>> # MultiGraph dict-of-dict-of-dict-of-attribute
>>> MDG = nx.MultiDiGraph()
>>> adj = {
...     1: {2: {0: {"weight": 1.3}, 1: {"weight": 1.2}}},
...     3: {2: {0: {"weight": 0.7}}},
... }
>>> e = [
...     (u, v, ekey, d)
...     for u, nbrs in adj.items()
...     for v, keydict in nbrs.items()
...     for ekey, d in keydict.items()
... ]
>>> MDG.update(edges=e)

See also

add_edges_from

add multiple edges to a graph

add_nodes_from

add multiple nodes to a graph

class wepy.resampling.resamplers.wexplore.WExploreResampler(seed=None, distance=None, max_region_sizes=None, init_state=None, pmin=1e-12, pmax=0.1, max_n_regions=(10, 10, 10, 10), **kwargs)

Bases: CloneMergeResampler

Resampler implementing the WExplore algorithm.

See the paper for a full description of the algorithm, but briefly:

WExplore defines a hierarchical Voronoi tesselation on a subspace of the full walker state. Regions in a Voronoi cell are defined by a point in this subspace called an ‘image’, and are scoped by their enclosing region in the hierarchy.

The hierarchy is defined initially by:

• number of levels of the hierarchy, AKA depth

• number of regions allowed at a level of the hierarchy

• a cutoff ‘distance’ at each level of the hierarchy

All regions have a unique specification (called a leaf_id) which is a k-tuple of region indices, where k is the depth of the hierarchy.

At first the hierarchy only has a single region at all levels which is given by the image of the ‘init_state’ constructor argument.

For a hierarchy of depth 4 the leaf_id for this first region is (0, 0, 0, 0) which indicates that at level 0 (the highest level) we are selecting the first region (region 0), and at level 1 we select the first region at that level (region 0 again), and so on.

For this region all images at each level are identical.

During resampling walkers first are binned into the region they fall. This is achieved using a breadth first search where the distance (according to the distance metric) between the walker state and all region images are computed. The image that is closest to the walker is selected and in the next iteration of comparisons we restrict the search to only regions within this super-region.

For example for a region tree with the following leaf ids: (0,0,0) and (0,1,0) we skip distance computations at level 0, since there is only one region. At level 1, we compute the distance to images 0 and 1 and choose the one that is closest. Since each of these regions only has 1 sub-region we do not need to recalculate the distance and can assign the walker.

Indeed every super-region will have exactly one sub-region that has the same image as it, and these distance calculations are never repeated for performance.

This resampler adds the additional ‘region_assignment’ field to the resampling records which indicates the region a walker was assigned to during resampling.

While walkers can always be assigned uniquely to a region the specification of the cutoff distances at each level indicate when sufficient novelty in a walker motivates creation of a new region.

The distances of the walker to each of the closest region images is saved for each level, e.g. (0.1, 0.3, 0.5) for the example above. This is compared to the cutoff distance specification, e.g. (0.2, 0.2, 0.2). The highest level at which a distance exceeds the cutoff will trigger region creation.

Following the example above the walker above exceeded the cutoff distance at level 1 and level 2 of the hierarchy, however level 1 takes precedence over the lower level.

This event of region creation can be thought of as a branching event of the tree, where the branching level is the level at which the branch occurred.

All branches of a region tree must extend the full depth and so the specification of the new branch can be given by the leaf_id of the region created, which would be (0, 2, 0) for this example.

The new image of this region is the image of the walker that triggered the branching.

Note that the ‘boundaries’ of the Voronoi cells are subject to change during branching.

The only limitation to this process is the allowed number of sub-regions for a super-region which is given for each level. For example, (5, 10, 10) indicates that regions at the top-most level can have 5 sub-regions, and in turn those sub-regions can have 10 sub-regions, and so on.

The resampler records give updates on the definitions of new regions and includes:

• branching_levelthe level of the tree the branching occured

  at, which relates it to the number of allowed regions and the cutoff distance new regions are made at.

• distancethe distance of the walker to the nearest region

  image that triggered the creation of a new region.

• new_leaf_idthe leaf id of the new region, which is a tuple of

  the index of each region index at each branching level.

• imagea datatype that stores the actual value of the newly

  created region.

That covers how regions are initialized, adaptively created, and recorded, but doesn’t explain how these regions are used inform the actual resampling process.

Essentially, the hierarchical structure allows for balanced resource trading between regions. The resource in the case of weighted ensemble is the allocation of a walker which will be scheduled for sampling in the next cycle. The more walkers a region has the more sampling of the region will occur.

After the sampling step walkers move around in regions and between regions. Some regions will end up collecting more walkers than other regions during this. The goal is to redistribute those walkers to other regions so that each level of the hierarchy is as balanced as possible.

So after sampling the number of walkers is added up for each region. At the top of the hierarchy a collection of trades between the super-regions is negotiated based on which regions are able to give up walkers and those that need them such that each region has as close to the same number of walkers as possible.

The ‘payment’ of a tax (or donation) is performed by merging walkers and the reception of the donation (or welfare dispensation) is achieved by cloning walkers.

Because there are constraints on how many walkers can be merged and cloned due to minimum and maximum walker probabilities and total number of walkers, sometimes a region may have an excess of walkers but none of them are taxable (donatable) because any merge would create a walker above the maximum probability. Conversely, a region may not be able to receive walkers because any clone of a walker would make walkers with weight lower than the minimum.

However, super-regions cannot actually ‘pay’ for these trades themselves and simply make a request to their sub-regions to provide the requested walkers (or to find room for accepting them). The trade negotiation process then repeats within each sub-region. When the request for debits and credits finally reaches leaf node regions the process stops and the actual identities of the walkers that will be cloned or merged are determined.

Then the cloning and merging of walkers is performed.

After this process if we were to recount the number of walkers in all regions then they should be pretty well balanced at each level.

Its worth noting that some regions will have no walkers because once a region contains no walkers (all walkers leave the region during sampling) it can no longer receive any walkers at all because it cannot clone. Of course walkers may re-enter the region and repopulate it but until that happens these regions are excluded from negotiations.

Only the net clones and merges are recorded in the records.

Constructor for the WExploreResampler.

Parameters:

• seed (None or int) – The random seed. If None the system (random) one will be used.

• distance (object implementing Distance) – The distance metric to compare walkers to region images with.

• init_state (WalkerState object) – The state that seeds the first region in the region hierarchy.

• max_n_regions (tuple of int) – The number of allowed sub-regions for a region at each level of the region hierarchy.

• max_region_sizes (tuple of float) – The cutoff distances that trigger the creation of new regions at each level of the hierarchy. Numbers dependent on the units of your distance metric. For example: (1, 0.5, 0.35, 0.25).

RESAMPLING_FIELDS = ('decision_id', 'target_idxs', 'step_idx', 'walker_idx', 'region_assignment')

String names of fields produced in this record group.

Resampling records are typically used to report on the details of how walkers are resampled for a given resampling step.

Warning

This is a critical function of many other components of the wepy framework and probably shouldn’t be altered by most developers.

Thi is where the information about cloning and merging of walkers is given. Seeing as this is a most of the value proposition of wepy as a tool getting rid of it will render most of the framework useless.

But sticking to the ‘loosely coupled, tightly integrated’ mantra you are free to modify these fields. This would be useful for implementing resampling strategies that do not follow basic cloning and merging. Just beware, that most of the lineage based analysis will be broken without implementing a new Decision class.

RESAMPLING_SHAPES = ((1,), Ellipsis, (1,), (1,), Ellipsis)

Numpy-style shapes of all fields produced in records.

There should be the same number of elements as there are in the corresponding ‘FIELDS’ class constant.

Each entry should either be:

1. A tuple of ints that specify the shape of the field element array.

2. Ellipsis, indicating that the field is variable length and limited to being a rank one array (e.g. (3,) or (1,)).

3. None, indicating that the first instance of this field will not be known until runtime. Any field that is returned by a record producing method will automatically interpreted as None if not specified here.

Note that the shapes must be tuple and not simple integers for rank-1 arrays.

Option B will result in the special h5py datatype ‘vlen’ and should not be used for large datasets for efficiency reasons.

RESAMPLING_DTYPES = (<class 'int'>, <class 'int'>, <class 'int'>, <class 'int'>, <class 'int'>)

Specifies the numpy dtypes to be used for records.

There should be the same number of elements as there are in the corresponding ‘FIELDS’ class constant.

Each entry should either be:

1. A numpy.dtype object.

4. None, indicating that the first instance of this field will not be known until runtime. Any field that is returned by a record producing method will automatically interpreted as None if not specified here.

RESAMPLING_RECORD_FIELDS = ('decision_id', 'target_idxs', 'step_idx', 'walker_idx', 'region_assignment')

Optional, names of fields to be selected for truncated representation of the record group.

These entries should be strings that are previously contained in the ‘FIELDS’ class constant.

While strictly no constraints on to which fields can be added here you should only choose those fields whose features could fit into a plaintext csv or similar format.

RESAMPLER_FIELDS = ('branching_level', 'distance', 'new_leaf_id')

String names of fields produced in this record group.

Resampler records are typically used to report on changes in the state of the resampler.

Notes

These fields are not critical to the proper functioning of the rest of the wepy framework and can be modified freely.

However, reporters specific to this resampler probably will make use of these records.

RESAMPLER_SHAPES = ((1,), (1,), Ellipsis, Ellipsis)

Numpy-style shapes of all fields produced in records.

There should be the same number of elements as there are in the corresponding ‘FIELDS’ class constant.

Each entry should either be:

1. A tuple of ints that specify the shape of the field element array.

2. Ellipsis, indicating that the field is variable length and limited to being a rank one array (e.g. (3,) or (1,)).

3. None, indicating that the first instance of this field will not be known until runtime. Any field that is returned by a record producing method will automatically interpreted as None if not specified here.

Note that the shapes must be tuple and not simple integers for rank-1 arrays.

Option B will result in the special h5py datatype ‘vlen’ and should not be used for large datasets for efficiency reasons.

RESAMPLER_DTYPES = (<class 'int'>, <class 'float'>, <class 'int'>, None)

Specifies the numpy dtypes to be used for records.

There should be the same number of elements as there are in the corresponding ‘FIELDS’ class constant.

Each entry should either be:

1. A numpy.dtype object.

4. None, indicating that the first instance of this field will not be known until runtime. Any field that is returned by a record producing method will automatically interpreted as None if not specified here.

RESAMPLER_RECORD_FIELDS = ('branching_level', 'distance', 'new_leaf_id')

Optional, names of fields to be selected for truncated representation of the record group.

These entries should be strings that are previously contained in the ‘FIELDS’ class constant.

While strictly no constraints on to which fields can be added here you should only choose those fields whose features could fit into a plaintext csv or similar format.

property region_tree

The RegionTree instance used to manage the region hierachy.

This is really only used internally to this class.

assign(walkers)

Assign walkers to regions in the tree, with region creation.

Parameters:

walkers (list of Walker objects)

Returns:

• assignments (list of tuple of int) – The leaf_id for each walker that it was assigned to.

• resampler_data (list of dict of str: value) – The list of resampler records recording each branching event.

CYCLE_DTYPES = (<class 'int'>, <class 'int'>)

Data types of the cycle fields

CYCLE_FIELDS = ('step_idx', 'walker_idx')

The fields that get added to the decision record for all resampling records. This places a record within a single destructured listing of records for a single cycle of resampling using the step and walker index.

CYCLE_RECORD_FIELDS = ('step_idx', 'walker_idx')

Optional, names of fields to be selected for truncated representation of the record group.

CYCLE_SHAPES = ((1,), (1,))

Data shapes of the cycle fields.

DEBUG_MODES = (True, False)

DECISION

alias of MultiCloneMergeDecision

_check_resampled_walkers(resampled_walkers)

Check constraints on resampled walkers.

Raises errors when constraints are violated.

Parameters:

resampled_walkers (list of Walker objects)

_init_walker_actions(n_walkers)

Returns a list of default resampling records for a single resampling step.

Parameters:

n_walkers (int) – The number of walkers to generate records for

Returns:

decision_records – A list of default decision records for one step of resampling.

Return type:

list of dict of str: value

_set_resampling_num_walkers(num_walkers)

Sets the concrete number of walkers constraints given a number of walkers and the settings for max and min.

Parameters:

num_walkers (int)

_unset_resampling_num_walkers()

assign_clones(merge_groups, walker_clone_nums)

Convert two convenient data structures to a list of almost normalized resampling records.

The two data structures are merge_groups and walker_clone_nums and are convenient to make.

Each is a list with number of elements equal to the number of walkers that resampling will act on.

Each element of the merge_groups is a list-like of integers indicating the indices of the walkers that will be merged into this one (i.e. squashed). A non-empty collection indicates a KEEP_MERGE decision.

Each element of the walker_clone_nums is simply an integer specifying how many clones to make of this walker.

These data structures simply declare requirements on what the actual decision records must achieve. The actual placement of walkers in slots (indices) is unspecified and immaterial.

Parameters:

• merge_groups (list of list of int) – The specification of which walkers will be squashed and merged.

• walker_clone_nums (list of int) – The number of clones to make for each walker.

Returns:

walker_actions – List of resampling record like dictionaries. These are not completely normalized for consumption by reporters, since they don’t have the right list-like wrappers.

Return type:

list of dict of str: values

debug_off()

debug_on()

decide(delta_walkers=0)

Make decisions for resampling for a single step.

Parameters:

delta_walkers (int) –

The net change in the number of walkers to make.

(Default value = 0)

Returns:

resampling_data – The resampling records resulting from the decisions.

Return type:

list of dict of str: value

property decision

The decision class for this resampler.

property is_debug_on

max_num_walkers()

“ Get the max number of walkers allowed currently

property max_num_walkers_setting

The specification for the maximum number of walkers for the resampler.

min_num_walkers()

“ Get the min number of walkers allowed currently

property min_num_walkers_setting

The specification for the minimum number of walkers for the resampler.

property pmax

property pmin

resampler_field_dtypes()

Access the class level DTYPES constant for this record group.

resampler_field_names()

Access the class level FIELDS constant for this record group.

resampler_field_shapes()

Access the class level SHAPES constant for this record group.

resampler_fields()

Returns a list of zipped field specs.

Returns:

record_specs – A list of the specs for each field, a spec is a tuple of type (field_name, shape_spec, dtype_spec)

Return type:

list of tuple

resampler_record_field_names()

Access the class level RECORD_FIELDS constant for this record group.

resampling_field_dtypes()

Access the class level DTYPES constant for this record group.

resampling_field_names()

Access the class level FIELDS constant for this record group.

resampling_field_shapes()

Access the class level SHAPES constant for this record group.

resampling_fields()

Returns a list of zipped field specs.

Returns:

record_specs – A list of the specs for each field, a spec is a tuple of type (field_name, shape_spec, dtype_spec)

Return type:

list of tuple

resampling_record_field_names()

Access the class level RECORD_FIELDS constant for this record group.

set_debug_mode(mode)

Parameters:

mode

static _check_resampling_data(resampling_data)

Parameters:

resampling_data

_resample_init(walkers=None)

Parameters:

walkers

_resample_cleanup(resampling_data=None, resampler_data=None, resampled_walkers=None)

Parameters:

• resampling_data

• resampler_data

• resampled_walkers

resample(walkers)

Perform resampling on the set of walkers.

Parameters:

• walkers (list of Walker objects) – The walkers that are to be resampled.

• debug_mode (bool) – Expert mode debugging setting, only forif you know exactly what you are doing.

Returns:

• resampled_walkers (list of Walker objects) – The set of resampled walkers

• resampling_data (list of dict of str: value) – A list of destructured resampling records from this round of resampling.

• resampler_data (list of dict of str: value) – A list of records recording how the state of the resampler was updated.