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
ornetworkx.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 edgeweight
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.
- verbosebool (default True)
if True, shows progress bars in loops and indication of steps
- **kwargs
kwargs for
networkx.betweenness_centrality
ornetworkx.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)