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A maximal matching is a set of independent edges such that the inclusion of any additional edge to the set violates the property of matching (no common vertex between any two edges of the set).
A maximal matching is a set of independent edges of the graph such that the inclusion of an additional edge to the set violates the property of matching (i.e., no two edges of a matching have a common end vertex) [12].
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The while loop in f′ or g′ is inevitable because it only takes as many iterations as there are matches to report the next time that The total number of set-maximal matches is bounded by NA, as required.
The A.Index of the maximal node matching is significantly low compared to that of the maximal assortative matching.
Likewise, the % of node matches observed with the maximal assortative matching is slightly larger than that obtained with the maximal dissortative matching for all operating conditions (the difference could be at most 7%%).
As explained in Sects. 1 and 2, the maximal node matching is independent of node weights; as a result, we expect the assortativity index of maximal node matching to be close to 0 for all values of (p_mathrm{link}) and it is confirmed through the simulations.
The maximal node matching for the random graphs (generated based on the Erdos Renyi model) with randomly assigned node weights (results analyzed in Sect. 5) incur an assortativity index close to 0 to vindicate that the maximal node matching is indeed independent of node weights.
Though the expected value for the assortative index of an MNM is 0 (to vindicate that the maximal node matching is independent of node weights); the assortativity index value of 0.55 observed for the graph in Fig. 4 is still far from 1 (an assortative index value of 1 would indicate the matching algorithm pairs nodes that are very dissimilar).
Thus, we conclude that the total time complexity of calculating the cohesion matrix using maximal weighted matching is O(n + nlog n) = O(nlog n).
As the worst case complexity for the maximal matching method is, the computation complexity for CES can be stated as.
A maximal matching that is arbitrary with respect to the weight of the vertices being matched need not be preferred in social networks.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com