相关论文: The Grand Canonical ensemble of weighted networks

Statistical ensembles of networks, i.e., probability spaces of all networks that are consistent with given aggregate statistics, have become instrumental in the analysis of complex networks. Their numerical and analytical study provides the…

The science of complex networks is a new interdisciplinary branch of science which has arisen recently on the interface of physics, biology, social and computer sciences, and others. Its main goal is to discover general laws governing the…

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…

Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes…

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…

One of the fundamental concepts in the statistical mechanics field is that of ensemble. Ensembles of graphs are collections of graphs, defined according to certain rules. The two most used ensembles in network theory are the microcanonical…

Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…

Complex networks in natural, social, and technological systems generically exhibit an abundance of rich information. Extracting meaningful structural features from data is one of the most challenging tasks in network theory. Many methods…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…

We present a new approach to the calculation of measures in weighted networks, based on the translation of a weighted network into an ensemble of edges. This leads to a straightforward generalization of any measure defined on unweighted…

Statistics of distinguishable particles has become relevant in systems of colloidal particles and in the context of applications of statistical mechanics to complex networks. When studying these type of systems with the standard textbook…

What do generic networks that have certain properties look like? We define Relative Canonical Network ensembles as the ensembles that realize a property R while being as indistinguishable as possible from a generic network ensemble. This…

A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…

Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…

In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to…

In this paper we define a new class of weighted complex networks sharing several properties with fractal sets, and whose topology can be completely analytically characterized in terms of the involved parameters and of the fractal dimension.…

When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or…

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…