temporal_closeness_centrality¶
Calculates temporal closeness centrality
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temporal_closeness_centrality(tnet=None, paths=None)[source]¶ Returns temporal closeness centrality per node.
Temporal closeness centrlaity is the sum of a node’s average temporal paths with all other nodes.
Parameters: - tnet (array, dict, object) – Temporal network input with nettype: ‘bu’, ‘bd’.
- paths (pandas dataframe) – Output of TenetoBIDS.networkmeasure.shortest_temporal_paths
Note
Only one input (tnet or paths) can be supplied to the function.
Returns: temporal closness centrality (nodal measure) Return type: close: array Notes
Temporal closeness centrality is defined in [Close-1]:
\[\begin{split}C^T_{i} = {{1} \over {N-1}}\sum_j{1\over\\tau_{ij}}\end{split}\]Where \(\\tau_{ij}\) is the average temporal paths between node i and j.
Note, there are multiple different types of temporal distance measures that can be used in temporal networks. If a temporal network is used as input (i.e. not the paths), then teneto uses
shortest_temporal_path()to calculates the shortest paths. Seeshortest_temporal_path()for more details.[Close-1] Pan, R. K., & Saramäki, J. (2011). Path lengths, correlations, and centrality in temporal networks. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 84(1). [`Link https://doi.org/10.1103/PhysRevE.84.016105`_]