Andrea Rapisarda

Bio: Andrea Rapisarda is an academic researcher from University of Catania. The author has contributed to research in topics: Mean field theory & Hamiltonian system. The author has an hindex of 36, co-authored 201 publications receiving 6804 citations. Previous affiliations of Andrea Rapisarda include Centra & University of Copenhagen.

Error and attack tolerance of complex networks

Abstract: 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 load). We consider and compare the results for two different network topologies: the Erdos–Renyi random graph and the Barabasi–Albert scale-free network. We also discuss briefly a dynamical model recently proposed to take into account the dynamical redistribution of loads after the initial damage of a single node of the network.

Efficiency of scale-free networks: error and attack tolerance

Abstract: The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e., networks with power law P(k), are considered: (1) scale-free networks with no local clustering produced by the Barabasi–Albert model and (2) scale-free networks with high clustering properties as in the model by Klemm and Eguiluz, and their properties are compared to the properties of random graphs (exponential graphs). By using as mathematical measures the global and the local efficiency we investigate the effects of errors and attacks both on the global and the local properties of the network. We show that the global efficiency is a better measure than the characteristic path length to describe the response of complex networks to external factors. We find that, at variance with random graphs, scale-free networks display, both on a global and on a local scale, a high degree of error tolerance and an extreme vulnerability to attacks. In fact, the global and the local efficiency are unaffected by the failure of some randomly chosen nodes, though they are extremely sensitive to the removal of the few nodes which play a crucial role in maintaining the network's connectivity.

Non-Gaussian equilibrium in a long-range Hamiltonian system.

Abstract: We study the dynamics of a system of N classical spins with infinite-range interaction We show that, if the thermodynamic limit is taken before the infinite-time limit, the system does not relax to the Boltzmann-Gibbs equilibrium, but exhibits different equilibrium properties, characterized by stable non-Gaussian velocity distributions, L\'evy walks, and dynamical correlation in phase space

Detecting complex network modularity by dynamical clustering

Abstract: Based on cluster desynchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort O(KN) on a generic graph with N nodes and K links.

Vector opinion dynamics in a bounded confidence consensus model

Abstract: We study the continuum opinion dynamics of the compromise model of Krause and Hegselmann for a community of mutually interacting agents by solving numerically a rate equation. The opinions are here represented by two-dimensional vectors with real-valued components. We study the situation starting from a uniform probability distribution for the opinion configuration and for different shapes of the confidence range. In all cases, we find that the thresholds for consensus and cluster merging either coincide with their one-dimensional counterparts, or are very close to them. The symmetry of the final opinion configuration, when more clusters survive, is determined by the shape of the opinion space. If the latter is a square, which is the case we consider, the clusters in general occupy the sites of a square lattice, although we sometimes observe interesting deviations from this general pattern, especially near the center of the opinion space.

Community detection in graphs

Abstract: The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

Network biology: understanding the cell's functional organization

Abstract: A key aim of postgenomic biomedical research is to systematically catalogue all molecules and their interactions within a living cell. There is a clear need to understand how these molecules and the interactions between them determine the function of this enormously complex machinery, both in isolation and when surrounded by other cells. Rapid advances in network biology indicate that cellular networks are governed by universal laws and offer a new conceptual framework that could potentially revolutionize our view of biology and disease pathologies in the twenty-first century.