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The Spearman's rank-based correlation coefficient (SCC) computed for maximal clique size and degree centrality for the example graph used from Figs. 1, 2, 3, 4 is 0.98.
Since both algorithms rely on finding the largest cliques in the graph induced by the state matrix, which as previously explained is known to be NP-complete in general, we have used the MATLAB function [40], which allows bounding the maximal clique size, hence bound the complexity according to Lemma 2. As baseline for comparison we used the traditional uncoded case.
Using Formulation 1, DELISHUS computes all inherited or de novo deletions with maximal clique size above a user-defined threshold and then ranks them according to a number of different properties.
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A clique-colouring of a graph is a colouring of its vertices such that no maximal clique of size at least two is monocoloured.
In other words: a clique-colouring of a graph is a colouring of its vertices such that no maximal clique of size at least two is monocoloured.
No maximal clique of size at least 2 is monocoloured since every maximal clique of G contains an induced subgraph isomorphic to a maximal clique of G′ that is not monocoloured by hypothesis.
Number of edges that belong to maximal cliques of size k.
Enumerating all maximal cliques with size no less than 3 is a NP-complete problem, and only non-polynomial time algorithms for solving it are known.
It needs an input parameter k between 1 and the number of nodes n with which the algorithm computes the clustering as follows: for any k between 1 and n compute all maximal cliques of size at least k.
Real: actual number of edges that belong to maximal cliques of size k; pred: predicted number of maximal k-clique edges; FD false discovery ratio): percentage of false-positives in the predicted set; FN false negative ratio): percentage of false-negatives in the real set.
In [ 40] it is defined as (2) B = C u C υ / C u, υ, where (u, υ) is the edge with u, υ being the endpoints, C uis the size of the maximal clique containing vertex u and C u, υ) is the size of the maximal clique containing (u, υ).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com