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 [Porta et al., 2006].
- Parameters:
- graphnetworkx.Graph
A Graph representing a street network. Ideally generated from GeoDataFrame using
momepy.gdf_to_nx()
.- namestr, optional
The calculated attribute name.
- modestr, default ‘nodes’
The mode of betweenness calculation.
'node'
for node-based or'edges'
for edge-based.- weightstr (default ‘mm_len’)
The 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 noden
duringego_graph
generation.- normalizedbool, optional
If
True
the betweenness values are normalized by 2/((n-1)(n-2)), wheren
is the number of nodes in a subgraph.- verbosebool (default True)
If
True
, shows progress bars in loops and indication of steps.- **kwargsdict
Keyword argument for
networkx.betweenness_centrality
ornetworkx.edge_betweenness_centrality
.
- Returns:
- netxGraph
A networkx.Graph object.
Notes
In case of angular betweenness, implementation is based on “Tasos Implementation”.
Examples
>>> network_graph = mm.betweenness_centrality(network_graph)