Package to estimate a minimum edge-disjoint edge clique cover (EECC) of a graph
Author giubuig
1 Star
Updated Last
26 Days Ago
Started In
April 2021


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This package DisjointCliqueCover, written in the Julia language, implements a method to estimate a minimal edge-disjoint edge clique cover (EECC) of a graph, according to the heuristic presented in Burgio et al. [1]. A minimal edge clique cover is a minimal set of cliques able to cover the entire set of edges in the graph. In a EECC, the cliques are required to be all edge-disjoint, i.e., they can have no more than one node in common.

A graph can admit multiple minimal edge clique covers and finding one of them is known to be a NP-complete problem. Therefore, approximate heuristics are needed to estimate it in large graphs.

The notion of EECC is introduced in [1] as a basis to define the Microscopic Epidemic Clique Equations (MECLE) model. This is a discrete-time markovian model describing complex contagion processes on higher-order networks, represented as hypergraphs and, specifically, as simplicial complexes. The model builds upon the cliques in the underlying graph of a considered higher-order network. As shown in [1], in order to account for the higher-order dynamical correlations among the states of the nodes in those cliques, the latter are required to be edje-disjoint. This leads to the search for the minimal EECC of the underlying graph, hence to the respective heuristic whose source code is here provided.


  1. Giulio Burgio, Alex Arenas, Sergio Gómez and Joan T. Matamalas: Network clique cover approximation to analyze complex contagions through group interactions, Comms. Phys. (2021) in press (arXiv:2101.03618)


  • Giulio Burgio (Universitat Rovira i Virgili, Tarragona, Spain)

  • Alex Arenas (Universitat Rovira i Virgili, Tarragona, Spain)

  • Sergio Gómez (Universitat Rovira i Virgili, Tarragona, Spain)

  • Joan T. Matamalas (Harvard Medical School & Brigham and Women's Hospital, Boston, USA)


The full documentation of DisjointCliqueCover.jl can be found here

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