favorite6(C) shows the material-only case with N = 0 (shown in Fig. The influence of long-range network topology greatly increases the complexity of the problem and obscures our understanding of the closeness between nodes in the sphere.
favorite0Figure 4: Fitting the heavy tail of the distribution of the nearest-neighbor GENs for the Barabasi-Albert networks in Fig. Over a wide range of values, there is an approximate power law decay which is very weakly dependent on N (N = 512 in the red circles and N = 1024 in the blue squares) but does depend on the average connectivity (hki = 4 shown above and hki = 20 below).
favorite3The centrality of individual nodes can also be measured incorporating the global topology of the network in a variety of ways, including PageRank, betweenness, or random walk centralities.
favorite14Community structure in networks can indicate the existence of underlying similarities between nodes in the network, and may have a great impact on dynamical processes occurring on the network (such as a random walk[14, 15, 16] or epidemic spreading[5, 17, 18]), and can influence the material properties of granular systems.