An analytical approach to network dynamics is used to show that when agents copy their state randomly, the network arrives to a stationary regime in which the distribution of states is independent of the degree. The effects of network topology on the process are characterized introducing a...

Power laws in socioeconomic systems are generally explained as being generated by multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumed to be...

A first characterization of the spectral properties of the Apollonian network is presented. Results are based on the numerically evaluated eigenvalue spectra of adjacency matrices for the first nine generations of the network. The main features refer to the presence of several gaps on the...

We study a model of wealth dynamics (Physica A 282 (2000) 536) which mimics transactions among economic agents. The outcomes of the model are shown to depend strongly on the topological properties of the underlying transaction network. The extreme cases of a fully connected and a fully...

We analyze the spectra of eigenvalues for random graphs with a local tree-like structure. The exact equations to the spectra of networks with a local tree-like structure are presented. We propose a simple approximation, and in the framework of effective medium approximation, calculate spectra of...

We study the synchronization of Kuramoto's oscillators in small parts of networks known as motifs. We first report on the system dynamics for the case of a scale-free network and show the existence of a non-trivial critical point. We compute the probability that network motifs synchronize, and...

Dynamics of a one-dimensional neural network with external periodic stimulation are investigated numerically. Synaptic connections with constant and random values were assumed. Three ranges of network dynamics—periodic, intermediate and chaotic—were found, depending on the number of...

A thesaurus is one, out of many, possible representations of term (or word) connectivity. The terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph. The directionality of the links retains all the thesaurus information and allows the measurement of...

Communication/transportation systems are often subjected to failures and attacks. Here we represent such systems as networks and we study their ability to resist failures (attacks) simulated as the breakdown of a group of nodes of the network chosen at random (chosen accordingly to degree or...