momepy.
local_betweenness_centrality
(graph, radius=5, name='betweenness', distance=None, weight=None, normalized=False, **kwargs)[source]¶Calculates the shortest-path betweenness centrality for nodes within subgraph.
Subgraph is generated around each node within set radius. If distance=None,
radius will define topological distance, otherwise it uses values in distance
attribute. Based on networkx.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}`, \(\sigma(s, t|v) = 0\).
Graph representing street network.
Ideally genereated from GeoDataFrame using momepy.gdf_to_nx()
number of topological steps defining the extent of subgraph
calculated attribute name
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.
Use the specified edge attribute as the edge distance in shortest path calculations in closeness centrality algorithm
If True the betweenness values are normalized by 2/((n-1)(n-2)), where n is the number of nodes in subgraph.
kwargs for networkx.betweenness_centrality_subset
networkx.Graph
Examples
>>> network_graph = mm.local_betweenness_centrality(network_graph, radius=800, distance='edge_length')