## Mercurial > repos > shellac > sam_consensus_v3

### view env/lib/python3.9/site-packages/networkx/algorithms/connectivity/utils.py @ 0:4f3585e2f14b draft default tip

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"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"

author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |

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""" Utilities for connectivity package """ import networkx as nx __all__ = ["build_auxiliary_node_connectivity", "build_auxiliary_edge_connectivity"] def build_auxiliary_node_connectivity(G): r"""Creates a directed graph D from an undirected graph G to compute flow based node connectivity. For an undirected graph G having `n` nodes and `m` edges we derive a directed graph D with `2n` nodes and `2m+n` arcs by replacing each original node `v` with two nodes `vA`, `vB` linked by an (internal) arc in D. Then for each edge (`u`, `v`) in G we add two arcs (`uB`, `vA`) and (`vB`, `uA`) in D. Finally we set the attribute capacity = 1 for each arc in D [1]_. For a directed graph having `n` nodes and `m` arcs we derive a directed graph D with `2n` nodes and `m+n` arcs by replacing each original node `v` with two nodes `vA`, `vB` linked by an (internal) arc (`vA`, `vB`) in D. Then for each arc (`u`, `v`) in G we add one arc (`uB`, `vA`) in D. Finally we set the attribute capacity = 1 for each arc in D. A dictionary with a mapping between nodes in the original graph and the auxiliary digraph is stored as a graph attribute: H.graph['mapping']. References ---------- .. [1] Kammer, Frank and Hanjo Taubig. Graph Connectivity. in Brandes and Erlebach, 'Network Analysis: Methodological Foundations', Lecture Notes in Computer Science, Volume 3418, Springer-Verlag, 2005. http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf """ directed = G.is_directed() mapping = {} H = nx.DiGraph() for i, node in enumerate(G): mapping[node] = i H.add_node(f"{i}A", id=node) H.add_node(f"{i}B", id=node) H.add_edge(f"{i}A", f"{i}B", capacity=1) edges = [] for (source, target) in G.edges(): edges.append((f"{mapping[source]}B", f"{mapping[target]}A")) if not directed: edges.append((f"{mapping[target]}B", f"{mapping[source]}A")) H.add_edges_from(edges, capacity=1) # Store mapping as graph attribute H.graph["mapping"] = mapping return H def build_auxiliary_edge_connectivity(G): """Auxiliary digraph for computing flow based edge connectivity If the input graph is undirected, we replace each edge (`u`,`v`) with two reciprocal arcs (`u`, `v`) and (`v`, `u`) and then we set the attribute 'capacity' for each arc to 1. If the input graph is directed we simply add the 'capacity' attribute. Part of algorithm 1 in [1]_ . References ---------- .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms. (this is a chapter, look for the reference of the book). http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf """ if G.is_directed(): H = nx.DiGraph() H.add_nodes_from(G.nodes()) H.add_edges_from(G.edges(), capacity=1) return H else: H = nx.DiGraph() H.add_nodes_from(G.nodes()) for (source, target) in G.edges(): H.add_edges_from([(source, target), (target, source)], capacity=1) return H