momepy.betweenness_centrality¶

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

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

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 [Porta et al., 2006].

Parameters:¶

graph : networkx.Graph¶

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

name : str, optional¶

The calculated attribute name.

mode : str, default 'nodes'¶

The mode of betweenness calculation. 'node' for node-based or 'edges' for edge-based.

weight : str (default 'mm_len')¶

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

radius : int¶

Include all neighbors of distance <= radius from n.

distance : str, 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.

normalized : bool, optional¶

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

verbose : bool (default True)¶

If True, shows progress bars in loops and indication of steps.

**kwargs : dict¶

Keyword argument for networkx.betweenness_centrality or networkx.edge_betweenness_centrality.

Returns:¶

netx – A networkx.Graph object.

Return type:¶

Graph

Examples

>>> network_graph = mm.betweenness_centrality(network_graph)

Notes

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