Related papers: Percolation on bipartite scale-free networks
We propose a multistage version of the independent cascade model, which we call a multistage independent cascade (MIC) model, on networks. This model is parameterized by two probabilities: the probability $T_1$ that a node adopting a fad…
Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation…
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network…
We investigate adjacency matrices of bipartite graphs with power-law degree distribution. Motivation for this study is twofold. First, vibrational states in granular matter and jammed sphere packings; second, graphs encoding social…
Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
In the field of complex networks, hypergraph models have so far received significantly less attention than graphs. However, many real-life networks feature multiary relations (co-authorship, protein reactions) may therefore be modeled way…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
It is widely believed that fractality of complex networks origins from hub repulsion behaviors (anticorrelation or disassortativity), which means large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
We study the site-bond percolation on a hierarchical scale-free network, namely, the decorated (2,2)-flower, by using the renormalization group technique. The phase diagram essentially depends on the fraction of occupied sites.…
Cascade models on networks have been used extensively to study cascade failure in complex systems. However, most current models consider failure caused by node damage and neglect the possibility of link damage, which is relevant to…
Our recent study on the Bethe lattice reported that a discontinuous percolation transition emerges as the number of occupied links increases and each node rewires its links to locally suppress the growth of neighboring clusters. However,…
Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…
We propose a bond-percolation model intended to describe the consumption, and eventual exhaustion, of resources in transport networks. Edges forming minimum-length paths connecting demanded origin-destination nodes are removed if below a…
A bootstrap percolation process on a graph $G$ is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round each uninfected node which has at least $r$ infected neighbours…
The internal organization of complex networks often has striking consequences on either their response to external perturbations or on their dynamical properties. In addition to small-world and scale-free properties, clustering is the most…
In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated…
We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…
We introduce the weighted random graph (WRG) model, which represents the weighted counterpart of the Erdos-Renyi random graph and provides fundamental insights into more complicated weighted networks. We find analytically that the WRG is…