momepy.
betweenness_centrality
(graph, name='betweenness', mode='nodes', weight='mm_len', endpoints=True, **kwargs)[source]¶Calculates the shortest-path betweenness centrality for nodes.
Wrapper around networkx.betweenness_centrality
or networkx.edge_betweenness_centrality
.
Betweenness centrality of a node v is the sum of the fraction of all-pairs shortest paths that pass through v
where V is the set of nodes, \(\sigma(s, t)\) is the number of shortest \((s, t)\)-paths, and \(\sigma(s, t|v)\) is the number of those paths passing through some node v other than s, t. If s = t, \(\sigma(s, t) = 1\), and if v in {s, t}`, \(\sigma(s, t|v) = 0\).
Betweenness centrality of an edge e is the sum of the fraction of all-pairs shortest paths that pass through e
where V is the set of nodes, \(\sigma(s, t)\) is the number of shortest \((s, t)\)-paths, and \(\sigma(s, t|e)\) is the number of those paths passing through edge e.
Graph representing street network.
Ideally genereated from GeoDataFrame using momepy.gdf_to_nx()
calculated attribute name
mode of betweenness calculation. ‘node’ for node-based, ‘edges’ for edge-based
attribute holding the weight of edge (e.g. length, angle)
kwargs for networkx.betweenness_centrality
or networkx.edge_betweenness_centrality
networkx.Graph
References
Porta S, Crucitti P and Latora V (2006) The network analysis of urban streets: A primal approach. Environment and Planning B: Planning and Design 33(5): 705–725.
Examples
>>> network_graph = mm.betweenness_centrality(network_graph)