## Mercurial > repos > shellac > sam_consensus_v3

### view env/lib/python3.9/site-packages/networkx/algorithms/bipartite/redundancy.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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"""Node redundancy for bipartite graphs.""" from itertools import combinations from networkx import NetworkXError __all__ = ["node_redundancy"] def node_redundancy(G, nodes=None): r"""Computes the node redundancy coefficients for the nodes in the bipartite graph `G`. The redundancy coefficient of a node `v` is the fraction of pairs of neighbors of `v` that are both linked to other nodes. In a one-mode projection these nodes would be linked together even if `v` were not there. More formally, for any vertex `v`, the *redundancy coefficient of `v`* is defined by .. math:: rc(v) = \frac{|\{\{u, w\} \subseteq N(v), \: \exists v' \neq v,\: (v',u) \in E\: \mathrm{and}\: (v',w) \in E\}|}{ \frac{|N(v)|(|N(v)|-1)}{2}}, where `N(v)` is the set of neighbors of `v` in `G`. Parameters ---------- G : graph A bipartite graph nodes : list or iterable (optional) Compute redundancy for these nodes. The default is all nodes in G. Returns ------- redundancy : dictionary A dictionary keyed by node with the node redundancy value. Examples -------- Compute the redundancy coefficient of each node in a graph:: >>> from networkx.algorithms import bipartite >>> G = nx.cycle_graph(4) >>> rc = bipartite.node_redundancy(G) >>> rc[0] 1.0 Compute the average redundancy for the graph:: >>> from networkx.algorithms import bipartite >>> G = nx.cycle_graph(4) >>> rc = bipartite.node_redundancy(G) >>> sum(rc.values()) / len(G) 1.0 Compute the average redundancy for a set of nodes:: >>> from networkx.algorithms import bipartite >>> G = nx.cycle_graph(4) >>> rc = bipartite.node_redundancy(G) >>> nodes = [0, 2] >>> sum(rc[n] for n in nodes) / len(nodes) 1.0 Raises ------ NetworkXError If any of the nodes in the graph (or in `nodes`, if specified) has (out-)degree less than two (which would result in division by zero, according to the definition of the redundancy coefficient). References ---------- .. [1] Latapy, Matthieu, ClĂ©mence Magnien, and Nathalie Del Vecchio (2008). Basic notions for the analysis of large two-mode networks. Social Networks 30(1), 31--48. """ if nodes is None: nodes = G if any(len(G[v]) < 2 for v in nodes): raise NetworkXError( "Cannot compute redundancy coefficient for a node" " that has fewer than two neighbors." ) # TODO This can be trivially parallelized. return {v: _node_redundancy(G, v) for v in nodes} def _node_redundancy(G, v): """Returns the redundancy of the node `v` in the bipartite graph `G`. If `G` is a graph with `n` nodes, the redundancy of a node is the ratio of the "overlap" of `v` to the maximum possible overlap of `v` according to its degree. The overlap of `v` is the number of pairs of neighbors that have mutual neighbors themselves, other than `v`. `v` must have at least two neighbors in `G`. """ n = len(G[v]) # TODO On Python 3, we could just use `G[u].keys() & G[w].keys()` instead # of instantiating the entire sets. overlap = sum( 1 for (u, w) in combinations(G[v], 2) if (set(G[u]) & set(G[w])) - {v} ) return (2 * overlap) / (n * (n - 1))