相关论文: The Intrinsic Scale of Networks is Small

Network reconstruction consists in retrieving the hidden interaction structure of a system from observations. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical…

Complex networks are usually characterized in terms of their topological, spatial, or information-theoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories.…

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…

Many real-world networks, including nervous systems, exhibit meso-scale structure. This means that their elements can be grouped into meaningful sub-networks. In general, these sub-networks are unknown ahead of time and must be "discovered"…

We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights…

We study the statistical properties of the sampled scale-free networks, deeply related to the proper identification of various real-world networks. We exploit three methods of sampling and investigate the topological properties such as…

Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…

Understanding key structural properties of large scale networks are crucial for analyzing and optimizing their performance, and improving their reliability and security. Here we show that these networks possess a previously unnoticed…

Meso-scale structures are network features where nodes with similar properties are grouped together instead of being treated individually. In this work, we provide formal and mathematical definitions of three such structures: assortative…

The structure of many financial networks is protected by privacy and has to be inferred from aggregate observables. Here we consider one of the most successful network reconstruction methods, producing random graphs with desired link…

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups…

The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…

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.…

Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…

High-throughput methods for yielding the set of connections in a neural system, the connectome, are now being developed. This tutorial describes ways to analyze the topological and spatial organization of the connectome at the macroscopic…

Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the…

To the best of our knowledge, this paper presents the first large-scale study that tests whether network categories (e.g., social networks vs. web graphs) are distinguishable from one another (using both categories of real-world networks…

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces.…

An identifying code of a graph is a dominating set which uniquely determines all the vertices by their neighborhood within the code. Whereas graphs with large minimum degree have small domination number, this is not the case for the…

Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…