Related papers: Classification of scale-free networks
Clustering and degree correlations are ubiquitous in real-world complex networks. Yet, understanding their role in critical phenomena remains a challenge for theoretical studies. Here, we provide the exact solution of site percolation in a…
In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution…
Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological…
The Japanese shareholding network at the end of March 2002 is studied. To understand the characteristics of this network intuitively, we visualize it as a directed graph and an adjacency matrix. Especially detailed features of networks…
Recent developments in graph theoretic analysis of complex networks have led to deeper understanding of brain networks. Many complex networks show similar macroscopic behaviors despite differences in the microscopic details. Probably two…
Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network.…
In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
We show that the connectivity distributions $P(k,t)$ of scale-free growing networks ($t$ is the network size) have the generic scale -- the cut-off at $k_{cut} \sim t^\beta$. The scaling exponent $\beta$ is related to the exponent $\gamma$…
In this letter, we proposed an ungrowing scale-free network model, wherein the total number of nodes is fixed and the evolution of network structure is driven by a rewiring process only. In spite of the idiographic form of $G$, by using a…
A variety of scale-free networks have been created since the pioneer work by A.-L. Barab\'{a}si and R. Albert. All this networks are homogeneous since they are composed of the same kind of nodes. In the realistic world, however, one element…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
Many biological, ecological and economic systems are best described by weighted networks, as the nodes interact with each other with varying strength. However, most network models studied so far are binary, the link strength being either 0…
In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the…
We study the traffic-driven epidemic spreading on scale-free networks with tunable degree distribution. The heterogeneity of networks is controlled by the exponent $\gamma$ of power-law degree distribution. It is found that the epidemic…
We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a…
In a recent work [arXiv:1307.1382] it was pointed out that the link-weight distribution of microRNA (miRNA) co-target network of a wide class of species are universal up to scaling. The number cell types, widely accepted as a measure of…
Food webs can be regarded as energy transporting networks in which the weight of each edge denotes the energy flux between two species. By investigating 21 empirical weighted food webs as energy flow networks, we found several ubiquitous…
In this letter, we investigate the detailed epidemic spreading process in scale-free networks with links' weights that denote familiarity between two individuals and find that spreading velocity reaches a peak quickly then decays in a…