Biomedical subjects

Ginestra Bianconi

Publications and source records attributed to Ginestra Bianconi.

8 recordsLinked to original sources

PubMed2006

Effect of degree correlations on the loop structure of scale-free networks.

In this paper we study the impact of degree correlations in the subgraph statistics of scale-free networks. In particular we consider loops, simple cases of network subgraphs which encode the redundancy of the paths passing through every two nodes of the network. We provide an understanding of the scaling of the clustering coefficient in modular networks in terms of the maximal eigenvector of the average adjacency matrix of the ensemble. Furthermore we show that correlations affect in a relevant way the average number of Hamiltonian paths in a three-core of real world networks. We prove our results in the two-vertex correlated hidden variable ensemble and we check the results with exact counting of small loops in real graphs.

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PubMed2006

Scale-free networks with an exponent less than two.

We study scale-free simple graphs with an exponent of the degree distribution gamma less than 2. Generically one expects such extremely skewed networks--which occur very frequently in systems of virtually or logically connected units--to have different properties than those of scale free networks with gamma>2: The number of links grows faster than the number of nodes and they naturally possess the small world property, because the diameter increases by the logarithm of the size of the network and the clustering coefficient is finite. We discuss a simple prototype model of such networks, inspired by real world phenomena, which exhibits these properties and allows for a detailed analytical investigation.

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PubMed2005

Loops structure of the Internet at the autonomous system level.

We present here a study of the clustering and loops in a graph of the Internet at the autonomous systems level. We show that, even if the whole structure is changing with time, the statistical distributions of loops of order 3, 4, and 5 remain stable during the evolution. Moreover, we will bring evidence that the Internet graphs show characteristic Markovian signatures, since the structure is very well described by two-point correlations between the degrees of the vertices. This indeed proves that the Internet belongs to a class of network in which the two-point correlation is sufficient to describe their whole local (and thus global) structure. Data are also compared to present Internet models.

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PubMed2004

Clogging and self-organized criticality in complex networks.

We propose a simple model that aims at describing, in a stylized manner, how local breakdowns due to imbalances or congestion propagate in real dynamical networks. The model converges to a self-organized critical stationary state in which the network shapes itself as a consequence of avalanches of rewiring processes. Depending on the model's specification, we obtain either single-scale or scale-free networks. We characterize in detail the relation between the statistical properties of the network and the nature of the critical state, by computing the critical exponents. The model also displays a nontrivial, sudden collapse to a complete network.

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PubMed2003

Size of quantum networks.

The metric structure of bosonic scale-free networks and fermionic Cayley-tree networks is analyzed, focusing on the directed distance of nodes from the origin. The topology of the networks strongly depends on the dynamical parameter T, called the temperature. At T= infinity we show analytically that the two networks have a similar behavior: the distance of a generic node from the origin of the network scales as the logarithm of the number of nodes in the network. At T=0 the two networks have an opposite behavior: the bosonic network remains very clusterized (the distance from the origin remains constant as the network increases the number of nodes), while the fermionic network grows following a single branch of the tree, and the distance from the origin varies as a power law of the number of nodes in the network.

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PubMed2003

Number of loops of size h in growing scale-free networks.

The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number N(h)(t) of loops of size h as a function of the system size. In particular, we have found the analytic expression for the scaling of N(h)(t) in the Barabási-Albert (BA) scale-free network. We have performed numerical simulations on the scaling law for N(h)(t) in the BA network and in other growing scale-free networks, such as the bosonic network and the aging nodes network. We show that in the bosonic network and in the aging node network the phase transitions in the topology of the network are accompained by a change in the scaling of the number of loops with the system size.

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PubMed2002

Quantum statistics in complex networks.

In this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics. This model takes into account the different nature of nodes, described by a random parameter that we call energy, and includes rewiring of the links. The system described by the mixed statistics is an inhomogeneous system formed by two class of nodes. In fact there is a threshold energy epsilon(s) such that nodes with lower energy (epsilon epsilon(s)) decrease their connectivity in time.

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PubMed2002

Growing Cayley trees described by a Fermi distribution.

In growing Cayley trees with thermal noise we show that the distribution of the bond strengths (energies) is described by the Fermi statistics. The evolution of these hierarchical networks reduces to the Eden model and the invasion percolation model in the limits T-->0 and T--> infinity, respectively. We discuss the relation of the present results with the scale-free networks described by Bose statistics.

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