momepy.betweenness_centrality

momepy.betweenness_centrality(graph, name='betweenness', mode='nodes', weight='mm_len', endpoints=True, radius=None, distance=None, normalized=False, **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

\[c_B(v) =\sum_{s,t \in V} \frac{\sigma(s, t|v)}{\sigma(s, t)}\]

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

\[c_B(e) =\sum_{s,t \in V} \frac{\sigma(s, t|e)}{\sigma(s, t)}\]

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.

Adapted from [PCL06].

Parameters
graphnetworkx.Graph

Graph representing street network. Ideally generated from GeoDataFrame using momepy.gdf_to_nx()

namestr, optional

calculated attribute name

modestr, default ‘nodes’

mode of betweenness calculation. ‘node’ for node-based, ‘edges’ for edge-based

weightstr (default ‘mm_len’)

attribute holding the weight of edge (e.g. length, angle)

radius: int

Include all neighbors of distance <= radius from n

distancestr, optional

Use specified edge data key as distance. For example, setting distance=’weight’ will use the edge weight to measure the distance from the node n during ego_graph generation.

normalizedbool, optional

If True the betweenness values are normalized by 2/((n-1)(n-2)), where n is the number of nodes in subgraph.

**kwargs

kwargs for networkx.betweenness_centrality or networkx.edge_betweenness_centrality

Returns
Graph

networkx.Graph

Notes

In case of angular betweenness, implementation is based on “Tasos Implementation”.

Examples

>>> network_graph = mm.betweenness_centrality(network_graph)