Spreading dynamics in heterogeneous graphs: Beyond the assortativity coefficient

We study spreading dynamics of a reaction-diffusion process in a special class of heterogeneous graphs with Poissonian degree distribution and composed of both local and long range links. The behavior of the spreading dynamics on such networks are investigated by relating them to the topological features of graphs. We find that the degree of assortativity can give just some indication about the large scale behavior of the spreading dynamics while a detailed description of the process can be addressed by introducing new, more appropriate, topological quantities linked to the distance between nodes.