Figure 1. m-cores decomposition and its visualization.

The example network in (a) is colored according to the m-coreness of nodes and edges. Nodes and edges colored in blue belong to the m0-core but not to the m1-core. Nodes and edges colored in green belong to the m1-core but not to the m2-core, etc. The same structure is represented in (b) with the visualization tool described in the main text. The outermost circle in blue represents the m0-core, with nodes of m-coreness 0 located in its perimeter. The m1-core –which is contained within the m0-core– is fragmented in two disconnected components, which are represented as two non-overlapping circles within the outermost one and with nodes of m-coreness 1 located in their perimeters. The larger of these two components is further fragmented in two disconnected components representing the m2-core and m3-core. The angular positions of nodes in each circumference are chosen to minimize the angular separation with their neighbors in different layers. Notice that in this representation, each edge is colored with two colors, corresponding to the colors of the m-coreness of the nodes at the end of the edge but in reverse order. In this way, it is possible to visualize easily connections between different layers. See27 for further details of the visualization.