arXiv subjects

R. Xulvi-Brunet

Publications and source records attributed to R. Xulvi-Brunet.

4 recordsLinked to original sources

arXiv2006

Growing networks under geographical constraints

Inspired by the structure of technological networks, we discuss network evolution mechanisms which give rise to topological properties found in real spatial networks. Thus, the peculiar structure of transport and distribution networks is fundamentally determined by two factors. These are the dependence of the spatial interaction range of vertices on the vertex attractiveness (or importance within the network) and on the inhomogeneous distribution of vertices in space. We propose and analyse numerically a simple model based on these generating mechanisms which seems, for instance, to be able to reproduce known structural features of the Internet.

physics.soc-ph↗

arXiv2004

Construction and properties of assortative random networks

Many social networks exhibit assortative mixing so that the predictions of uncorrelated models might be inadequate. To analyze the role of assortativity we introduce an algorithm which changes correlations in a network and produces assortative mixing to a desired degree. This degree is governed by one parameter p. Changing this parameter one can construct networks ranging from fully random (p = 0) to totally assortative (p = 1). We apply the algorithm to a Barabasi-Albert scale-free network and show that the degree of assortativity is an important parameter governing geometrical and transport properties of networks. Thus, the diameter of the network and the clustering coefficient increase dramatically with the degree of assortativity. Moreover, the concentration dependences of the size of the giant component in the node percolation problem for uncorrelated and assortative networks are strongly different.

cond-mat.stat-mech↗

arXiv2003

Correlations in Scale-Free Networks: Tomography and Percolation

We discuss three related models of scale-free networks with the same degree distribution but different correlation properties. Starting from the Barabasi-Albert construction based on growth and preferential attachment we discuss two other networks emerging when randomizing it with respect to links or nodes. We point out that the Barabasi-Albert model displays dissortative behavior with respect to the nodes' degrees, while the node-randomized network shows assortative mixing. These kinds of correlations are visualized by discussig the shell structure of the networks around their arbitrary node. In spite of different correlation behavior, all three constructions exhibit similar percolation properties.

cond-mat.stat-mech↗

arXiv2002

Evolving networks with disadvantaged long-range connections

We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at distance $d$ is proportional to $d^{-α}$, where $α$ is a tunable parameter of the model. We show that the properties of the networks grown with $α<1$ are close to those of the genuine scale-free construction, while for $α>1$ the structure of the network is vastly different. Thus, in this regime, the node degree distribution is no more a power law, and it is well-represented by a stretched exponential. On the other hand, the small-world property of the growing networks is preserved at all values of $α$.

cond-mat.stat-mech↗