Related papers: Spectra of complex networks
In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose $G_1, G_2, G_3, \ldots$ is a sequence of finite and connected graphs that share a common universal cover $T$ and such that…
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…
Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes…
We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and derive a new formula for the Stieljes transform of the spectral…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
For many complex networks present in nature only a single instance, usually of large size, is available. Any measurement made on this single instance cannot be repeated on different realizations. In order to detect significant patterns in a…
We review the behavior of epidemic spreading on complex networks in which there are explicit correlations among the degrees of connected vertices.
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…
Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains…
This article describes a gradient complex network model whose weights are proportional to the difference between uniformly distributed ``fitness'' values assigned to the nodes. It is shown analytically and experimentally that the strength…
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it…
The concept of 'complexity' plays a central role in complex network science. Traditionally, this term has been taken to express heterogeneity of the node degrees of a therefore complex network. However, given that the degree distribution is…
The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree…
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
Spectra of real world networks exhibit properties which are different from the random networks. One such property is the existence of a very high degeneracy at zero eigenvalues. In this work, we provide possible reasons behind occurrence of…
We present an analysis of the spectral density of the adjacency matrix of large random trees. We show that there is an infinity of delta peaks at all real numbers which are eigenvalues of finite trees. By exact enumerations and Monte-Carlo…
Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Core-periphery structure is an emerging property of a wide range of complex systems and indicate the presence of group of actors in the system with an higher number of connections among them and a lower number of connections with a sparsely…
The importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…