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Author: Aric Hagberg (hagberg@lanl.gov) Pieter Swart (swart@lanl.gov) Sasha Gutfraind (ag362@cornell.edu)
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Compute the betweenness centrality for nodes in G: the fraction of number of shortests paths that pass through each node. The keyword normalized (default=True) specifies whether the betweenness values are normalized by b=b/(n-1)(n-2) where n is the number of nodes in G. The keyword weighted_edges (default=False) specifies whether to use edge weights (otherwise weights are all assumed equal). The algorithm is from Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163-177, 2001. http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf |
"Load" centrality for nodes. This actually computes 'load' and not betweenness. See https://networkx.lanl.gov/ticket/103 The fraction of number of shortests paths that go through each node counted according to the algorithm in Scientific collaboration networks: II. Shortest paths, weighted networks, and centrality, M. E. J. Newman, Phys. Rev. E 64, 016132 (2001). Returns a dictionary of betweenness values keyed by node. The betweenness is normalized to be between [0,1]. If normalized=False the resulting betweenness is not normalized. If weighted_edges is True then use Dijkstra for finding shortest paths. |
Node betweenness helper: see betweenness_centrality for what you probably want. This actually computes "load" and not betweenness. See https://networkx.lanl.gov/ticket/103 This calculates the load of each node for paths from a single source. (The fraction of number of shortests paths from source that go through each node.) To get the load for a node you need to do all-pairs shortest paths. If weighted_edges is True then use Dijkstra for finding shortest paths. In this case a cutoff is not implemented and so is ignored. |
Compute the betweenness centrality for nodes in G: the fraction of number of shortests paths that pass through each node. The keyword normalized (default=True) specifies whether the betweenness values are normalized by b=b/(n-1)(n-2) where n is the number of nodes in G. The keyword weighted_edges (default=False) specifies whether to use edge weights (otherwise weights are all assumed equal). The algorithm is from Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163-177, 2001. http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf |
"Load" centrality for nodes. This actually computes 'load' and not betweenness. See https://networkx.lanl.gov/ticket/103 The fraction of number of shortests paths that go through each node counted according to the algorithm in Scientific collaboration networks: II. Shortest paths, weighted networks, and centrality, M. E. J. Newman, Phys. Rev. E 64, 016132 (2001). Returns a dictionary of betweenness values keyed by node. The betweenness is normalized to be between [0,1]. If normalized=False the resulting betweenness is not normalized. If weighted_edges is True then use Dijkstra for finding shortest paths. |
Enchanced version of the method in centrality module that allows specifying a list of sources (subgraph). weighted_edges:: consider edge weights by running Dijkstra's algorithm (no effect on unweighted graphs). sources:: list of nodes to consider as subgraph See Sec. 4 in Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163-177, 2001. http://www.inf.uni-konstanz.de/algo/publications/b-fabc-01.pdf This algorithm does not count the endpoints, i.e. a path from s to t does not contribute to the betweenness of s and t. |
Edge betweenness centrality. weighted_edges:: consider edge weights by running Dijkstra's algorithm (no effect on unweighted graphs). sources:: list of nodes to consider as subgraph |
Helper for betweenness centrality and edge betweenness centrality. Runs single-source shortest path from root node. weighted_edges:: consider edge weights Finds: S=[] list of nodes reached during traversal P={} predecessors, keyed by child node D={} distances sigma={} indexed by node, is the number of paths to root going through the node |
Edge Betweenness WARNING: This module is for demonstration and testing purposes. |
Degree centrality for nodes (fraction of nodes connected to). Returns a dictionary of degree centrality values keyed by node. The degree centrality is normalized to the maximum possible degree in the graph G. |
Closeness centrality for nodes (1/average distance to all nodes). Returns a dictionary of closeness centrality values keyed by node. The closeness centrality is normalized to be between 0 and 1. |
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