Source code for networkx.classes.multigraph

"""Base class for MultiGraph."""
#    Copyright (C) 2004-2011 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
from copy import deepcopy
import networkx as nx
from networkx.classes.graph import Graph
from networkx import NetworkXError
__author__ = """\n""".join(['Aric Hagberg (hagberg@lanl.gov)',
                            'Pieter Swart (swart@lanl.gov)',
                            'Dan Schult(dschult@colgate.edu)'])

[docs]class MultiGraph(Graph): """ An undirected graph class that can store multiedges. Multiedges are multiple edges between two nodes. Each edge can hold optional data or attributes. A MultiGraph holds undirected edges. Self loops are allowed. Nodes can be arbitrary (hashable) Python objects with optional key/value attributes. Edges are represented as links between nodes with optional key/value attributes. Parameters ---------- data : input graph Data to initialize graph. If data=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 NumPy matrix or 2d ndarray, a SciPy sparse matrix, or a PyGraphviz graph. attr : keyword arguments, optional (default= no attributes) Attributes to add to graph as key=value pairs. See Also -------- Graph DiGraph MultiDiGraph Examples -------- Create an empty graph structure (a "null graph") with no nodes and no edges. >>> G = nx.MultiGraph() G can be grown in several ways. **Nodes:** Add one node at a time: >>> G.add_node(1) Add the nodes from any container (a list, dict, set or even the lines from a file or the nodes from another graph). >>> G.add_nodes_from([2,3]) >>> G.add_nodes_from(range(100,110)) >>> H=nx.Graph() >>> H.add_path([0,1,2,3,4,5,6,7,8,9]) >>> G.add_nodes_from(H) In addition to strings and integers any hashable Python object (except None) can represent a node, e.g. a customized node object, or even another Graph. >>> G.add_node(H) **Edges:** G can also be grown by adding edges. Add one edge, >>> G.add_edge(1, 2) a list of edges, >>> G.add_edges_from([(1,2),(1,3)]) or a collection of edges, >>> G.add_edges_from(H.edges()) If some edges connect nodes not yet in the graph, the nodes are added automatically. If an edge already exists, an additional edge is created and stored using a key to identify the edge. By default the key is the lowest unused integer. >>> G.add_edges_from([(4,5,dict(route=282)), (4,5,dict(route=37))]) >>> G[4] {3: {0: {}}, 5: {0: {}, 1: {'route': 282}, 2: {'route': 37}}} **Attributes:** Each graph, node, and edge can hold key/value attribute pairs in an associated attribute dictionary (the keys must be hashable). By default these are empty, but can be added or changed using add_edge, add_node or direct manipulation of the attribute dictionaries named graph, node and edge respectively. >>> G = nx.MultiGraph(day="Friday") >>> G.graph {'day': 'Friday'} Add node attributes using add_node(), add_nodes_from() or G.node >>> G.add_node(1, time='5pm') >>> G.add_nodes_from([3], time='2pm') >>> G.node[1] {'time': '5pm'} >>> G.node[1]['room'] = 714 >>> del G.node[1]['room'] # remove attribute >>> G.nodes(data=True) [(1, {'time': '5pm'}), (3, {'time': '2pm'})] Warning: adding a node to G.node does not add it to the graph. Add edge attributes using add_edge(), add_edges_from(), subscript notation, or G.edge. >>> G.add_edge(1, 2, weight=4.7 ) >>> G.add_edges_from([(3,4),(4,5)], color='red') >>> G.add_edges_from([(1,2,{'color':'blue'}), (2,3,{'weight':8})]) >>> G[1][2][0]['weight'] = 4.7 >>> G.edge[1][2][0]['weight'] = 4 **Shortcuts:** Many common graph features allow python syntax to speed reporting. >>> 1 in G # check if node in graph True >>> [n for n in G if n<3] # iterate through nodes [1, 2] >>> len(G) # number of nodes in graph 5 >>> G[1] # adjacency dict keyed by neighbor to edge attributes ... # Note: you should not change this dict manually! {2: {0: {'weight': 4}, 1: {'color': 'blue'}}} The fastest way to traverse all edges of a graph is via adjacency_iter(), but the edges() method is often more convenient. >>> for n,nbrsdict in G.adjacency_iter(): ... for nbr,keydict in nbrsdict.items(): ... for key,eattr in keydict.items(): ... if 'weight' in eattr: ... (n,nbr,eattr['weight']) (1, 2, 4) (2, 1, 4) (2, 3, 8) (3, 2, 8) >>> [ (u,v,edata['weight']) for u,v,edata in G.edges(data=True) if 'weight' in edata ] [(1, 2, 4), (2, 3, 8)] **Reporting:** Simple graph information is obtained using methods. Iterator versions of many reporting methods exist for efficiency. Methods exist for reporting nodes(), edges(), neighbors() and degree() as well as the number of nodes and edges. For details on these and other miscellaneous methods, see below. """
[docs] def add_edge(self, u, v, key=None, attr_dict=None, **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 providing a dictionary with key/value pairs. See examples below. Parameters ---------- u,v : nodes Nodes can be, for example, strings or numbers. Nodes must be hashable (and not None) Python objects. key : hashable identifier, optional (default=lowest unused integer) Used to distinguish multiedges between a pair of nodes. attr_dict : dictionary, optional (default= no attributes) Dictionary of edge attributes. Key/value pairs will update existing data associated with the edge. 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 ----- To replace/update edge data, use the optional key argument to identify a unique edge. Otherwise a new edge will be created. NetworkX algorithms designed for weighted graphs cannot use multigraphs directly because it is not clear how to handle multiedge weights. Convert to Graph using edge attribute 'weight' to enable weighted graph algorithms. 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, 2, key=0, weight=4) # update data for key=0 >>> G.add_edge(1, 3, weight=7, capacity=15, length=342.7) """ # set up attribute dict if attr_dict is None: attr_dict=attr else: try: attr_dict.update(attr) except AttributeError: raise NetworkXError(\ "The attr_dict argument must be a dictionary.") # add nodes if u not in self.adj: self.adj[u] = {} self.node[u] = {} if v not in self.adj: self.adj[v] = {} self.node[v] = {} if v in self.adj[u]: keydict=self.adj[u][v] if key is None: # find a unique integer key # other methods might be better here? key=len(keydict) while key in keydict: key+=1 datadict=keydict.get(key,{}) datadict.update(attr_dict) keydict[key]=datadict else: # selfloops work this way without special treatment if key is None: key=0 datadict={} datadict.update(attr_dict) keydict={key:datadict} self.adj[u][v] = keydict self.adj[v][u] = keydict
[docs] def add_edges_from(self, ebunch, attr_dict=None, **attr): """Add all the edges in ebunch. Parameters ---------- ebunch : container of edges Each edge given in the container will be added to the graph. The edges can be: - 2-tuples (u,v) or - 3-tuples (u,v,d) for an edge attribute dict d, or - 4-tuples (u,v,k,d) for an edge identified by key k attr_dict : dictionary, optional (default= no attributes) Dictionary of edge attributes. Key/value pairs will update existing data associated with each edge. 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 edges as a tuple take precedence over attributes specified generally. 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') """ # set up attribute dict if attr_dict is None: attr_dict=attr else: try: attr_dict.update(attr) except AttributeError: raise NetworkXError(\ "The attr_dict argument must be a dictionary.") # process ebunch for e in ebunch: ne=len(e) if ne==4: u,v,key,dd = e elif ne==3: u,v,dd = e key=None elif ne==2: u,v = e dd = {} key=None else: raise NetworkXError(\ "Edge tuple %s must be a 2-tuple, 3-tuple or 4-tuple."%(e,)) if u in self.adj: keydict=self.adj[u].get(v,{}) else: keydict={} if key is None: # find a unique integer key # other methods might be better here? key=len(keydict) while key in keydict: key+=1 datadict=keydict.get(key,{}) datadict.update(attr_dict) datadict.update(dd) self.add_edge(u,v,key=key,attr_dict=datadict)
[docs] def remove_edge(self, u, v, key=None): """Remove an edge between u and v. Parameters ---------- u,v: nodes Remove an edge between nodes u and v. key : hashable identifier, optional (default=None) Used to distinguish multiple edges between a pair of nodes. If None remove a single (abritrary) edge between u and v. Raises ------ NetworkXError If there is not an edge between u and v, or if there is no edge with the specified key. See Also -------- remove_edges_from : remove a collection of edges Examples -------- >>> G = nx.MultiGraph() >>> G.add_path([0,1,2,3]) >>> G.remove_edge(0,1) >>> e = (1,2) >>> G.remove_edge(*e) # unpacks e from an edge tuple For multiple edges >>> G = nx.MultiGraph() # or MultiDiGraph, etc >>> G.add_edges_from([(1,2),(1,2),(1,2)]) >>> G.remove_edge(1,2) # remove a single (arbitrary) edge For edges with keys >>> G = nx.MultiGraph() # or MultiDiGraph, etc >>> G.add_edge(1,2,key='first') >>> G.add_edge(1,2,key='second') >>> G.remove_edge(1,2,key='second') """ try: d=self.adj[u][v] except (KeyError): raise NetworkXError( "The edge %s-%s is not in the graph."%(u,v)) # remove the edge with specified data if key is None: d.popitem() else: try: del d[key] except (KeyError): raise NetworkXError( "The edge %s-%s with key %s is not in the graph."%(u,v,key)) if len(d)==0: # remove the key entries if last edge del self.adj[u][v] if u!=v: # check for selfloop del self.adj[v][u]
[docs] def remove_edges_from(self, 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) All edges between u and v are removed. - 3-tuples (u,v,key) The edge identified by key is removed. - 4-tuples (u,v,key,data) where data 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.MultiGraph() # or MultiDiGraph >>> G.add_path([0,1,2,3]) >>> ebunch=[(1,2),(2,3)] >>> G.remove_edges_from(ebunch) Removing multiple copies of edges >>> G = nx.MultiGraph() >>> G.add_edges_from([(1,2),(1,2),(1,2)]) >>> G.remove_edges_from([(1,2),(1,2)]) >>> G.edges() [(1, 2)] >>> G.remove_edges_from([(1,2),(1,2)]) # silently ignore extra copy >>> G.edges() # now empty graph [] """ for e in ebunch: try: self.remove_edge(*e[:3]) except NetworkXError: pass
[docs] def has_edge(self, u, v, key=None): """Return True if the graph has an edge between nodes u and v. Parameters ---------- u,v : nodes Nodes can be, for example, strings or numbers. key : hashable identifier, optional (default=None) If specified return True only if the edge with key is found. Returns ------- edge_ind : bool True if edge is in the graph, False otherwise. Examples -------- Can be called either using two nodes u,v, an edge tuple (u,v), or an edge tuple (u,v,key). >>> G = nx.MultiGraph() # or MultiDiGraph >>> G.add_path([0,1,2,3]) >>> G.has_edge(0,1) # using two nodes True >>> e = (0,1) >>> G.has_edge(*e) # e is a 2-tuple (u,v) True >>> G.add_edge(0,1,key='a') >>> G.has_edge(0,1,key='a') # specify key True >>> e=(0,1,'a') >>> G.has_edge(*e) # e is a 3-tuple (u,v,'a') 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 """ try: if key is None: return v in self.adj[u] else: return key in self.adj[u][v] except KeyError: return False
[docs] def edges(self, nbunch=None, data=False, keys=False): """Return a list of edges. Edges are returned as tuples with optional data and keys in the order (node, neighbor, key, data). Parameters ---------- nbunch : iterable container, optional (default= all nodes) A container of nodes. The container will be iterated through once. data : bool, optional (default=False) Return two tuples (u,v) (False) or three-tuples (u,v,data) (True). keys : bool, optional (default=False) Return two tuples (u,v) (False) or three-tuples (u,v,key) (True). Returns -------- edge_list: list of edge tuples Edges that are adjacent to any node in nbunch, or a list of all edges if nbunch is not specified. See Also -------- edges_iter : return an iterator over the 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.MultiGraph() # or MultiDiGraph >>> G.add_path([0,1,2,3]) >>> G.edges() [(0, 1), (1, 2), (2, 3)] >>> G.edges(data=True) # default edge data is {} (empty dictionary) [(0, 1, {}), (1, 2, {}), (2, 3, {})] >>> G.edges(keys=True) # default keys are integers [(0, 1, 0), (1, 2, 0), (2, 3, 0)] >>> G.edges(data=True,keys=True) # default keys are integers [(0, 1, 0, {}), (1, 2, 0, {}), (2, 3, 0, {})] >>> G.edges([0,3]) [(0, 1), (3, 2)] >>> G.edges(0) [(0, 1)] """ return list(self.edges_iter(nbunch, data=data,keys=keys))
[docs] def edges_iter(self, nbunch=None, data=False, keys=False): """Return an iterator over the edges. Edges are returned as tuples with optional data and keys in the order (node, neighbor, key, data). Parameters ---------- nbunch : iterable container, optional (default= all nodes) A container of nodes. The container will be iterated through once. data : bool, optional (default=False) If True, return edge attribute dict with each edge. keys : bool, optional (default=False) If True, return edge keys with each edge. Returns ------- edge_iter : iterator An iterator of (u,v), (u,v,d) or (u,v,key,d) tuples of edges. See Also -------- edges : return a list of 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.MultiGraph() # or MultiDiGraph >>> G.add_path([0,1,2,3]) >>> [e for e in G.edges_iter()] [(0, 1), (1, 2), (2, 3)] >>> list(G.edges_iter(data=True)) # default data is {} (empty dict) [(0, 1, {}), (1, 2, {}), (2, 3, {})] >>> list(G.edges(keys=True)) # default keys are integers [(0, 1, 0), (1, 2, 0), (2, 3, 0)] >>> list(G.edges(data=True,keys=True)) # default keys are integers [(0, 1, 0, {}), (1, 2, 0, {}), (2, 3, 0, {})] >>> list(G.edges_iter([0,3])) [(0, 1), (3, 2)] >>> list(G.edges_iter(0)) [(0, 1)] """ seen={} # helper dict to keep track of multiply stored edges if nbunch is None: nodes_nbrs = self.adj.items() else: nodes_nbrs=((n,self.adj[n]) for n in self.nbunch_iter(nbunch)) if data: for n,nbrs in nodes_nbrs: for nbr,keydict in nbrs.items(): if nbr not in seen: for key,data in keydict.items(): if keys: yield (n,nbr,key,data) else: yield (n,nbr,data) seen[n]=1 else: for n,nbrs in nodes_nbrs: for nbr,keydict in nbrs.items(): if nbr not in seen: for key,data in keydict.items(): if keys: yield (n,nbr,key) else: yield (n,nbr) seen[n] = 1 del seen
[docs] def get_edge_data(self, u, v, key=None, default=None): """Return the attribute dictionary associated with edge (u,v). Parameters ---------- u,v : nodes default: any Python object (default=None) Value to return if the edge (u,v) is not found. key : hashable identifier, optional (default=None) Return data only for the edge with specified key. Returns ------- edge_dict : dictionary The edge attribute dictionary. Notes ----- It is faster to use G[u][v][key]. >>> G = nx.MultiGraph() # or MultiDiGraph >>> G.add_edge(0,1,key='a',weight=7) >>> G[0][1]['a'] # key='a' {'weight': 7} Warning: Assigning G[u][v][key] corrupts the graph data structure. But it is safe to assign attributes to that dictionary, >>> G[0][1]['a']['weight'] = 10 >>> G[0][1]['a']['weight'] 10 >>> G[1][0]['a']['weight'] 10 Examples -------- >>> G = nx.MultiGraph() # or MultiDiGraph >>> G.add_path([0,1,2,3]) >>> G.get_edge_data(0,1) {0: {}} >>> e = (0,1) >>> G.get_edge_data(*e) # tuple form {0: {}} >>> G.get_edge_data('a','b',default=0) # edge not in graph, return 0 0 """ try: if key is None: return self.adj[u][v] else: return self.adj[u][v][key] except KeyError: return default
[docs] def degree_iter(self, nbunch=None, weight=None): """Return an iterator for (node, degree). The node degree is the number of edges adjacent to the node. Parameters ---------- nbunch : iterable container, optional (default=all nodes) A container of nodes. The container will be iterated through once. 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. The degree is the sum of the edge weights adjacent to the node. Returns ------- nd_iter : an iterator The iterator returns two-tuples of (node, degree). See Also -------- degree Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> list(G.degree_iter(0)) # node 0 with degree 1 [(0, 1)] >>> list(G.degree_iter([0,1])) [(0, 1), (1, 2)] """ if nbunch is None: nodes_nbrs = self.adj.items() else: nodes_nbrs=((n,self.adj[n]) for n in self.nbunch_iter(nbunch)) if weight is None: for n,nbrs in nodes_nbrs: deg = sum([len(data) for data in nbrs.values()]) yield (n, deg+(n in nbrs and len(nbrs[n]))) else: # edge weighted graph - degree is sum of nbr edge weights for n,nbrs in nodes_nbrs: deg = sum([d.get(weight,1) for data in nbrs.values() for d in data.values()]) if n in nbrs: deg += sum([d.get(weight,1) for key,d in nbrs[n].items()]) yield (n, deg)
def is_multigraph(self): """Return True if graph is a multigraph, False otherwise.""" return True def is_directed(self): """Return True if graph is directed, False otherwise.""" return False
[docs] def to_directed(self): """Return a directed representation of the graph. Returns ------- G : MultiDiGraph 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). 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, http://docs.python.org/library/copy.html. Examples -------- >>> G = nx.Graph() # or MultiGraph, etc >>> G.add_path([0,1]) >>> H = G.to_directed() >>> H.edges() [(0, 1), (1, 0)] If already directed, return a (deep) copy >>> G = nx.DiGraph() # or MultiDiGraph, etc >>> G.add_path([0,1]) >>> H = G.to_directed() >>> H.edges() [(0, 1)] """ from networkx.classes.multidigraph import MultiDiGraph G=MultiDiGraph() G.add_nodes_from(self) G.add_edges_from( (u,v,key,deepcopy(datadict)) for u,nbrs in self.adjacency_iter() for v,keydict in nbrs.items() for key,datadict in keydict.items() ) G.graph=deepcopy(self.graph) G.node=deepcopy(self.node) return G
[docs] def selfloop_edges(self, data=False, keys=False): """Return a list of selfloop edges. A selfloop edge has the same node at both ends. Parameters ----------- data : bool, optional (default=False) Return selfloop edges as two tuples (u,v) (data=False) or three-tuples (u,v,data) (data=True) keys : bool, optional (default=False) If True, return edge keys with each edge. Returns ------- edgelist : list of edge tuples A list of all selfloop edges. See Also -------- nodes_with_selfloops, number_of_selfloops Examples -------- >>> G = nx.MultiGraph() # or MultiDiGraph >>> G.add_edge(1,1) >>> G.add_edge(1,2) >>> G.selfloop_edges() [(1, 1)] >>> G.selfloop_edges(data=True) [(1, 1, {})] >>> G.selfloop_edges(keys=True) [(1, 1, 0)] >>> G.selfloop_edges(keys=True, data=True) [(1, 1, 0, {})] """ if data: if keys: return [ (n,n,k,d) for n,nbrs in self.adj.items() if n in nbrs for k,d in nbrs[n].items()] else: return [ (n,n,d) for n,nbrs in self.adj.items() if n in nbrs for d in nbrs[n].values()] else: if keys: return [ (n,n,k) for n,nbrs in self.adj.items() if n in nbrs for k in nbrs[n].keys()] else: return [ (n,n) for n,nbrs in self.adj.items() if n in nbrs for d in nbrs[n].values()]
[docs] def number_of_edges(self, u=None, v=None): """Return the number of edges between two nodes. Parameters ---------- u,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 : int The number of edges in the graph. If nodes u and v are specified return the number of edges between those nodes. See Also -------- size Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> G.number_of_edges() 3 >>> G.number_of_edges(0,1) 1 >>> e = (0,1) >>> G.number_of_edges(*e) 1 """ if u is None: return self.size() try: edgedata=self.adj[u][v] except KeyError: return 0 # no such edge return len(edgedata)
[docs] def subgraph(self, nbunch): """Return the subgraph induced on nodes in nbunch. The induced subgraph of the graph contains the nodes in nbunch and the edges between those nodes. Parameters ---------- nbunch : list, iterable A container of nodes which will be iterated through once. Returns ------- G : Graph A subgraph of the graph with the same edge attributes. Notes ----- The graph, edge or node attributes just point to the original graph. So changes to the node or edge structure will not be reflected in the original graph while changes to the attributes will. To create a subgraph with its own copy of the edge/node attributes use: nx.Graph(G.subgraph(nbunch)) If edge attributes are containers, a deep copy can be obtained using: G.subgraph(nbunch).copy() For an inplace reduction of a graph to a subgraph you can remove nodes: G.remove_nodes_from([ n in G if n not in set(nbunch)]) Examples -------- >>> G = nx.Graph() # or DiGraph, MultiGraph, MultiDiGraph, etc >>> G.add_path([0,1,2,3]) >>> H = G.subgraph([0,1,2]) >>> H.edges() [(0, 1), (1, 2)] """ bunch =self.nbunch_iter(nbunch) # create new graph and copy subgraph into it H = self.__class__() # copy node and attribute dictionaries for n in bunch: H.node[n]=self.node[n] # namespace shortcuts for speed H_adj=H.adj self_adj=self.adj # add nodes and edges (undirected method) for n in H: Hnbrs={} H_adj[n]=Hnbrs for nbr,edgedict in self_adj[n].items(): if nbr in H_adj: # add both representations of edge: n-nbr and nbr-n # they share the same edgedict ed=edgedict.copy() Hnbrs[nbr]=ed H_adj[nbr][n]=ed H.graph=self.graph return H