Robustness of the avalanche dynamics in data packet transport on scale-free networks

We study the avalanche dynamics in the data packet transport on scale-free networks through a simple model. In the model, each vertex is assigned a capacity proportional to the load with a proportionality constant $1+a$. When the system is perturbed by a single vertex removal, the load of each vertex is redistributed, followed by subsequent failures of overloaded vertices. The avalanche size depends on the parameter $a$ as well as which vertex triggers it. We find that there exists a critical value $a_c$ at which the avalanche size distribution follows a power law. The critical exponent associated with it appears to be robust as long as the degree exponent is between 2 and 3, and is close in value to that of the distribution of the diameter changes by single vertex removal.Comment: 5 pages, 7 figures, final version published in PR

Branching process approach for Boolean bipartite networks of metabolic reactions

The branching process (BP) approach has been successful in explaining the avalanche dynamics in complex networks. However, its applications are mainly focused on unipartite networks, in which all nodes are of the same type. Here, motivated by a need to understand avalanche dynamics in metabolic networks, we extend the BP approach to a particular bipartite network composed of Boolean AND and OR logic gates. We reduce the bipartite network into a unipartite network by integrating out OR gates, and obtain the effective branching ratio for the remaining AND gates. Then the standard BP approach is applied to the reduced network, and the avalanche size distribution is obtained. We test the BP results with simulations on the model networks and two microbial metabolic networks, demonstrating the usefulness of the BP approach

Classification of scale-free networks

While the emergence of a power law degree distribution in complex networks is intriguing, the degree exponent is not universal. Here we show that the betweenness centrality displays a power-law distribution with an exponent \eta which is robust and use it to classify the scale-free networks. We have observed two universality classes with \eta \approx 2.2(1) and 2.0, respectively. Real world networks for the former are the protein interaction networks, the metabolic networks for eukaryotes and bacteria, and the co-authorship network, and those for the latter one are the Internet, the world-wide web, and the metabolic networks for archaea. Distinct features of the mass-distance relation, generic topology of geodesics and resilience under attack of the two classes are identified. Various model networks also belong to either of the two classes while their degree exponents are tunable.Comment: 6 Pages, 6 Figures, 1 tabl

Betweenness centrality correlation in social networks

Scale-free (SF) networks exhibiting a power-law degree distribution can be grouped into the assortative, dissortative and neutral networks according to the behavior of the degree-degree correlation coefficient. Here we investigate the betweenness centrality (BC) correlation for each type of SF networks. While the BC-BC correlation coefficients behave similarly to the degree-degree correlation coefficients for the dissortative and neutral networks, the BC correlation is nontrivial for the assortative ones found mainly in social networks. The mean BC of neighbors of a vertex with BC $g_i$ is almost independent of $g_i$, implying that each person is surrounded by almost the same influential environments of people no matter how influential the person is.Comment: 4 pages, 4 figures, 1 tabl

Nonlocal evolution of weighted scale-free networks

We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the network is determined nonlocally, this approach can explain the generic nonlinear scaling between the strength and the degree of a node. We demonstrate by a simple model that the strength-driven evolution scheme recently introduced can be generalized to a nonlinear preferential attachment rule, generating the power-law behaviors in degree and in strength simultaneously.Comment: 4 pages, 4 figures, final version published in PR