Related papers: Power-law relations in random networks with commun…
Complex networks as the World Wide Web, the web of human sexual contacts or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local…
Given a network and a partition in communities, we consider the issues "how communities influence each other" and "when two given communities do communicate". Specifically, we address these questions in the context of small-world networks,…
Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
Many real networks are equipped with short diameters, high clustering, and power-law degree distributions. With preferential attachment and network growth, the model by Barabasi and Albert simultaneously reproduces these properties, and…
A simple but powerful network model with $n$ nodes and $m$ partly overlapping layers is generated as an overlay of independent random graphs $G_1,\dots,G_m$ with variable sizes and densities. The model is parameterised by a joint…
The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these…
Many networks in nature, society and technology are characterized by a mesoscopic level of organization, with groups of nodes forming tightly connected units, called communities or modules, that are only weakly linked to each other.…
In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. This hypothesis is based not only on the general observation that many real networks have multilevel…
Stimulated by the growing interest in the applications of complex networks framework on time series analysis, we devise a network model in which each of $N$ nodes is associated with a random walk of length $L$. Connectivity between any two…
Complex networks have recently aroused a lot of interest. However, network edges are considered to be the same in almost all these studies. In this paper, we present a simple classification method, which divides the edges of undirected,…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
The rapidly developing theory of complex networks indicates that real networks are not random, but have a highly robust large-scale architecture, governed by strict organizational principles. Here, we focus on the properties of biological…
Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…
Modularity is a quantity which has been introduced in the context of complex networks in order to quantify how close a network is to an ideal modular network in which the nodes form small interconnected communities that are joined together…
The degree distribution of a real world network -- the number of links per node -- often follows a power law, with some hubs having many more links than traditional graph generation methods predict. For years, preferential attachment and…
Hypergraphs, describing networks where interactions take place among any number of units, are a natural tool to model many real-world social and biological systems. In this work we propose a principled framework to model the organization of…
For most networks, the connection between two nodes is the result of their mutual affinity and attachment. In this paper, we propose a mutual selection model to characterize the weighted networks. By introducing a general mechanism of…
The scaling relation derived by Dorogovtsev, Goltsev, Mendes and Samukhin [Phys. Rev. E, 68 (2003) 046109] states that the exponents of the power-law connectivity distribution, gamma, and the power-law eigenvalue distribution of the…
The topological (graph) structure of complex networks often provides valuable information about the performance and vulnerability of the network. However, there are multiple ways to represent a given network as a graph. Electric power…