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The median value for the A.Index of the maximal matching obtained with the MAM algorithm across the six real-world network graphs is 0.76, while the median value for the A.Index of the maximal matching obtained with the MNM algorithm is 0.17.
Figures 5, 6, 7, 8, 9 and 10 illustrate the maximal matching obtained for each of the real-world network graphs with respect to both maximal node matching and maximal assortative matching.
We assume the node weights as node degree and calculate the assortativity index (hereafter, shortly referred to as A.Index) of the network (considering the set of all edges) and the assortativity index of the maximal matching obtained with the MAM and MNM algorithms.
For each (p_mathrm{link}) value, we run 100 trials of the network evolution and analyze the assortatvity of the network as well as evaluate the % of node matches and assortativity of the maximal matching obtained with both the MAM and MNM algorithms.
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Note that the MNM algorithm is independent of the node weights as the assortativity weight for an edge is measured simply to be the number of uncovered adjacent edges; thus, the maximal node matching obtained using the MNM algorithm for a given graph would be the same irrespective of the criterion used for node weights.
Average sizes of maximal unique matches obtained by MUMmer PROmer (supplementary material, Supplementary Material online) are similar to average gene sizes indicating absence of synteny.
For each of the six real-world graphs, the MAM algorithm yielded a maximal matching that had a significantly larger A.Index compared to the matching obtained with the MNM algorithm.
Neglecting the negative A.Index values obtained for the maximal matching to the Karate Club network under both the algorithms, the range of A.Index values obtained with the MAM algorithm across the other five real-world network graphs is 0.50 0.87, whereas the range of A.Index values obtained with the MNM algorithm across these real-world network graphs is 0.23 to 0.51.
This simplification relates the minimum-length scheduling problem to the problem of obtaining a maximal matching in a non-bipartite graph [11].
When the RN is placed at each shared region, the optimal relay assignment can be obtained by utilizing the maximal matching method.
The maximal matching algorithm for maximizing the assortativity index (hereafter, referred to as the maximal assortative matching algorithm, MAM) prefers to include edges that have lower assortativity weight as part of the matching.
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