Related papers: Variational principle for scale-free network motif…

Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…

We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible.…

We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that…

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…

We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We…

Network motifs are often called the building blocks of networks. Analysis of motifs is found to be an indispensable tool for understanding local network structure, in contrast to measures based on node degree distribution and its functions…

In this work we introduce an energy function in order to study finite scale free graphs generated with different models. The energy distribution has a fractal pattern and presents log periodic oscillations for high energies. This…

We provide a framework for modeling social network formation through conditional multinomial logit models from discrete choice and random utility theory, in which each new edge is viewed as a "choice" made by a node to connect to another…

We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the…

The observation that some subgraphs, called motifs, appear more often in real networks than in their randomized counterparts has attracted much attention in the scientific community. In the prevalent approach the detection of motifs is…

The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are…

A wide variety of real-life networks share two remarkable generic topological properties: scale-free behavior and modular organization, and it is natural and important to study how these two features affect the dynamical processes taking…

We propose a simple dynamical model that generates networks with power-law degree distributions with the exponent 2 through rewiring only. At each time step, two nodes, i and j, are randomly selected, and one incoming link to i is…

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…

We consider the problem of selecting a minimum size subset of nodes in a network, that allows to activate all the nodes of the network. We present a fast and simple algorithm that, in real-life networks, produces solutions that outperform…

Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…

Data series motif discovery represents one of the most useful primitives for data series mining, with applications to many domains, such as robotics, entomology, seismology, medicine, and climatology, and others. The state-of-the-art motif…

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…

In this paper we show how The Free Energy Principle (FEP) can provide an explanation for why real-world networks deviate from scale-free behaviour, and how these characteristic deviations can emerge from constraints on information…

Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…