Source code for networkx.algorithms.operators.binary

"""
Operations on graphs including union, intersection, difference.
"""
import networkx as nx

__all__ = [
    "union",
    "compose",
    "disjoint_union",
    "intersection",
    "difference",
    "symmetric_difference",
    "full_join",
]


[docs]def union(G, H, rename=(None, None), name=None): """Return the union of graphs G and H. Graphs G and H must be disjoint, otherwise an exception is raised. Parameters ---------- G,H : graph A NetworkX graph rename : bool , default=(None, None) Node names of G and H can be changed by specifying the tuple rename=('G-','H-') (for example). Node "u" in G is then renamed "G-u" and "v" in H is renamed "H-v". name : string Specify the name for the union graph Returns ------- U : A union graph with the same type as G. Notes ----- To force a disjoint union with node relabeling, use disjoint_union(G,H) or convert_node_labels_to integers(). Graph, edge, and node attributes are propagated from G and H to the union graph. If a graph attribute is present in both G and H the value from H is used. See Also -------- disjoint_union """ if not G.is_multigraph() == H.is_multigraph(): raise nx.NetworkXError("G and H must both be graphs or multigraphs.") # Union is the same type as G R = G.__class__() # add graph attributes, H attributes take precedent over G attributes R.graph.update(G.graph) R.graph.update(H.graph) # rename graph to obtain disjoint node labels def add_prefix(graph, prefix): if prefix is None: return graph def label(x): if isinstance(x, str): name = prefix + x else: name = prefix + repr(x) return name return nx.relabel_nodes(graph, label) G = add_prefix(G, rename[0]) H = add_prefix(H, rename[1]) if set(G) & set(H): raise nx.NetworkXError( "The node sets of G and H are not disjoint.", "Use appropriate rename=(Gprefix,Hprefix)" "or use disjoint_union(G,H).", ) if G.is_multigraph(): G_edges = G.edges(keys=True, data=True) else: G_edges = G.edges(data=True) if H.is_multigraph(): H_edges = H.edges(keys=True, data=True) else: H_edges = H.edges(data=True) # add nodes R.add_nodes_from(G) R.add_nodes_from(H) # add edges R.add_edges_from(G_edges) R.add_edges_from(H_edges) # add node attributes for n in G: R.nodes[n].update(G.nodes[n]) for n in H: R.nodes[n].update(H.nodes[n]) return R
[docs]def disjoint_union(G, H): """Return the disjoint union of graphs G and H. This algorithm forces distinct integer node labels. Parameters ---------- G,H : graph A NetworkX graph Returns ------- U : A union graph with the same type as G. Notes ----- A new graph is created, of the same class as G. It is recommended that G and H be either both directed or both undirected. The nodes of G are relabeled 0 to len(G)-1, and the nodes of H are relabeled len(G) to len(G)+len(H)-1. Graph, edge, and node attributes are propagated from G and H to the union graph. If a graph attribute is present in both G and H the value from H is used. """ R1 = nx.convert_node_labels_to_integers(G) R2 = nx.convert_node_labels_to_integers(H, first_label=len(R1)) R = union(R1, R2) R.graph.update(G.graph) R.graph.update(H.graph) return R
[docs]def intersection(G, H): """Returns a new graph that contains only the nodes and the edges that exist in both G and H. Parameters ---------- G,H : graph A NetworkX graph. G and H can have different node sets but must be both graphs or both multigraphs. Raises ------ NetworkXError If one is a MultiGraph and the other one is a graph. Returns ------- GH : A new graph with the same type as G. Notes ----- Attributes from the graph, nodes, and edges are not copied to the new graph. If you want a new graph of the intersection of G and H with the attributes (including edge data) from G use remove_nodes_from() as follows >>> G = nx.path_graph(3) >>> H = nx.path_graph(5) >>> R = G.copy() >>> R.remove_nodes_from(n for n in G if n not in H) >>> R.remove_edges_from(e for e in G.edges if e not in H.edges) """ if not G.is_multigraph() == H.is_multigraph(): raise nx.NetworkXError("G and H must both be graphs or multigraphs.") # create new graph if set(G) != set(H): R = G.__class__() R.add_nodes_from(set(G.nodes).intersection(set(H.nodes))) else: R = nx.create_empty_copy(G) if G.number_of_edges() <= H.number_of_edges(): if G.is_multigraph(): edges = G.edges(keys=True) else: edges = G.edges() for e in edges: if H.has_edge(*e): R.add_edge(*e) else: if H.is_multigraph(): edges = H.edges(keys=True) else: edges = H.edges() for e in edges: if G.has_edge(*e): R.add_edge(*e) return R
[docs]def difference(G, H): """Returns a new graph that contains the edges that exist in G but not in H. The node sets of H and G must be the same. Parameters ---------- G,H : graph A NetworkX graph. G and H must have the same node sets. Returns ------- D : A new graph with the same type as G. Notes ----- Attributes from the graph, nodes, and edges are not copied to the new graph. If you want a new graph of the difference of G and H with the attributes (including edge data) from G use remove_nodes_from() as follows: >>> G = nx.path_graph(3) >>> H = nx.path_graph(5) >>> R = G.copy() >>> R.remove_nodes_from(n for n in G if n in H) """ # create new graph if not G.is_multigraph() == H.is_multigraph(): raise nx.NetworkXError("G and H must both be graphs or multigraphs.") R = nx.create_empty_copy(G) if set(G) != set(H): raise nx.NetworkXError("Node sets of graphs not equal") if G.is_multigraph(): edges = G.edges(keys=True) else: edges = G.edges() for e in edges: if not H.has_edge(*e): R.add_edge(*e) return R
[docs]def symmetric_difference(G, H): """Returns new graph with edges that exist in either G or H but not both. The node sets of H and G must be the same. Parameters ---------- G,H : graph A NetworkX graph. G and H must have the same node sets. Returns ------- D : A new graph with the same type as G. Notes ----- Attributes from the graph, nodes, and edges are not copied to the new graph. """ # create new graph if not G.is_multigraph() == H.is_multigraph(): raise nx.NetworkXError("G and H must both be graphs or multigraphs.") R = nx.create_empty_copy(G) if set(G) != set(H): raise nx.NetworkXError("Node sets of graphs not equal") gnodes = set(G) # set of nodes in G hnodes = set(H) # set of nodes in H nodes = gnodes.symmetric_difference(hnodes) R.add_nodes_from(nodes) if G.is_multigraph(): edges = G.edges(keys=True) else: edges = G.edges() # we could copy the data here but then this function doesn't # match intersection and difference for e in edges: if not H.has_edge(*e): R.add_edge(*e) if H.is_multigraph(): edges = H.edges(keys=True) else: edges = H.edges() for e in edges: if not G.has_edge(*e): R.add_edge(*e) return R
[docs]def compose(G, H): """Returns a new graph of G composed with H. Composition is the simple union of the node sets and edge sets. The node sets of G and H do not need to be disjoint. Parameters ---------- G, H : graph A NetworkX graph Returns ------- C: A new graph with the same type as G Notes ----- It is recommended that G and H be either both directed or both undirected. Attributes from H take precedent over attributes from G. For MultiGraphs, the edges are identified by incident nodes AND edge-key. This can cause surprises (i.e., edge `(1, 2)` may or may not be the same in two graphs) if you use MultiGraph without keeping track of edge keys. """ if not G.is_multigraph() == H.is_multigraph(): raise nx.NetworkXError("G and H must both be graphs or multigraphs.") R = G.__class__() # add graph attributes, H attributes take precedent over G attributes R.graph.update(G.graph) R.graph.update(H.graph) R.add_nodes_from(G.nodes(data=True)) R.add_nodes_from(H.nodes(data=True)) if G.is_multigraph(): R.add_edges_from(G.edges(keys=True, data=True)) else: R.add_edges_from(G.edges(data=True)) if H.is_multigraph(): R.add_edges_from(H.edges(keys=True, data=True)) else: R.add_edges_from(H.edges(data=True)) return R
[docs]def full_join(G, H, rename=(None, None)): """Returns the full join of graphs G and H. Full join is the union of G and H in which all edges between G and H are added. The node sets of G and H must be disjoint, otherwise an exception is raised. Parameters ---------- G, H : graph A NetworkX graph rename : bool , default=(None, None) Node names of G and H can be changed by specifying the tuple rename=('G-','H-') (for example). Node "u" in G is then renamed "G-u" and "v" in H is renamed "H-v". Returns ------- U : The full join graph with the same type as G. Notes ----- It is recommended that G and H be either both directed or both undirected. If G is directed, then edges from G to H are added as well as from H to G. Note that full_join() does not produce parallel edges for MultiGraphs. The full join operation of graphs G and H is the same as getting their complement, performing a disjoint union, and finally getting the complement of the resulting graph. Graph, edge, and node attributes are propagated from G and H to the union graph. If a graph attribute is present in both G and H the value from H is used. See Also -------- union disjoint_union """ R = union(G, H, rename) def add_prefix(graph, prefix): if prefix is None: return graph def label(x): if isinstance(x, str): name = prefix + x else: name = prefix + repr(x) return name return nx.relabel_nodes(graph, label) G = add_prefix(G, rename[0]) H = add_prefix(H, rename[1]) for i in G: for j in H: R.add_edge(i, j) if R.is_directed(): for i in H: for j in G: R.add_edge(i, j) return R