# momepy.local_closeness_centrality¶

momepy.local_closeness_centrality(graph, radius=5, name='closeness', distance=None, weight=None)[source]

Calculates local closeness for each node based on the defined distance.

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.closeness_centrality.

Local closeness centrality of a node u is the reciprocal of the average shortest path distance to u over all n-1 nodes within subgraph.

$C(u) = \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},$

where d(v, u) is the shortest-path distance between v and u, and n is the number of nodes that can reach u.

Parameters
graphnetworkx.Graph

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

number of topological steps defining the extent of subgraph

namestr, optional

calculated attribute name

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.

weightstr, optional

Use the specified edge attribute as the edge distance in shortest path calculations in closeness centrality algorithm

Returns
Graph

networkx.Graph

References

Porta S, Crucitti P and Latora V (2006) The network analysis of urban streets: A primal approach. Environment and Planning B: Planning and Design 33(5): 705–725.

Examples

>>> network_graph = mm.local_closeness_centrality(network_graph, radius=400, distance='edge_length')