Abbas Shoja-Daliklidash, Morteza Nattagh-Najafi, Nasser Sepehri-Javan

In this paper, we address a longstanding challenge in self-organized criticality (SOC) systems: establishing a connection between sandpiles and complex networks. Our approach employs a similarity-based transfer function characterized by two parameters, =(r1,r2). Here, r1 quantifies the similarity of local activities, while r2 governs the filtration process used to convert a weighted network into a binary one. We reveal that the degree centrality distribution of the resulting network follows a generalized Gamma distribution (GGD), which transitions to a power-law distribution under specific conditions. The GGD exponents, estimated numerically, exhibit a dependency on . Notably, while both decreasing r1 and r2 lead to denser networks, r2 plays a more significant role in influencing network density. Furthermore, the Shannon entropy is observed to decrease linearly with increasing r2, whereas its variation with r1 is more gradual. An analytical expression for the Shannon entropy is proposed. To characterize the network structure, we investigate the clustering coefficient (cc), eigenvalue centrality (e), closeness centrality (c), and betweenness centrality (b). The distributions of cc, e, and c exhibit peaked profiles, while b displays a power-law distribution over a finite interval of k. Additionally, we explore correlations between the exponents and identify a specific parameter regime of  and k where the e−k, c−k, and b−k correlations become negative.

Read the full article at: arxiv.org

• Papers