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Graph Decompositions Analysis and Comparison for Cohesive Subgraphs Detection

Massive networks have shown that the determination of dense subgraphs, where vertices interact a lot, is necessary in order to visualize groups of common interest, and therefore be able to decompose a big graph into smaller structures. Many decompositions have been built over the years as part of research in the graph mining field, and the topic is becoming a trend in the last decade because of the increasing size of social networks and databases. Here, we analyse some of the decompositions methods and also present a novel one, the Vertex Triangle k-core. We then compare them and test them against each other. Moreover, we establish different kind of measures for comparing the accuracy of the decomposition methods. We apply these decompositions to real world graphs, like the Collaboration network of arXiv graph, and found some interesting results.