  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.
