Calculates the centrality (fraction of intercepted flows) of all subgraphs on L vertices of a graph.
Updated 13 Jan 2018

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This function calculates the centralities of all connected induced subgraphs on L vertices of a (weighted di)graph as per the article "Loop-centrality in economic and biological networks", to appear in the Proceedings of the Sixth International Conference on Complex Networks and Their Applications, also available at
We recall that the centrality of cycle c or subgraph H is defined as the fraction of all networks flows intercepted by c (or H), that is passing through at least once by at least one vertex of c (or H). Equivalently, this fraction asymptotically determines the number of hikes on the entire graph, which are walks left-multiples of the prime c, in the context of the semi-commutative extension of number theory valid for walks on graphs ("Algebraic Combinatorics on Trace Monoids: Extending Number Theory to Walks on Graphs", SIAM J. Discrete Math., 31(2), 1428–1453).
To only compute the centralities of a few selected subgraphs or cycles, use the function FlowFraction on the File Exchange.
USAGE: SubgraphCentrality(A,L0,SaveCoordinates), A the adjacency matrix of the (weighted di)graph, L0 the size of the subgraphs for which the centrality is desired. Set SaveCoordinates to 0 if you do not wish to access the coordinates of the subgraphs, any other value will save the coordinates. All results are saved in a file 'CentralityResults.mat'.

Cite As

Pierre-Louis Giscard (2024). SubgraphCentrality(A,L0,SaveCoordinates) (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2017a
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes

Corrected a minor mistake in the joining of two cells, preventing the proper saving of the coordinates in certain cases where the data exceed a set size.