A. Santiago

An extended formalism for preferential attachment in heterogeneous complex networks

In this paper we present a framework for the extension of the Barabasi-Albert model to heterogeneous complex networks. We define a class of heterogeneous preferential attachment models where node properties are described by fixed states in an arbitrary space, and introduce an affinity function that biases the attachment probabilities of links. We perform an analytical study of the degree distributions in heterogeneous preferential attachment networks. We show that their degree densities exhibit a richer scaling behavior than their homogeneous counterparts, and that the power law scaling in the degree distribution is robust in the presence of heterogeneity.

EMERGENCE OF MULTISCALING IN HETEROGENEOUS COMPLEX NETWORKS

In this paper we provide numerical evidence of the richer behavior of the connectivity degrees in heterogeneous preferential attachment networks in comparison to their homogeneous counterparts. We analyze the degree distribution in the threshold model, a preferential attachment model where the affinity between node states biases the attachment probabilities of links. We show that the degree densities exhibit a power-law multiscaling which points to a signature of heterogeneity in preferential attachment networks. This translates into a power-law scaling in the degree distribution, whose exponent depends on the specific form of heterogeneity in the attachment mechanism.

MODELING THE TOPOLOGY OF SDH NETWORKS

SDH (Synchronous Digital Hierarchy) is the standard technology for the information transmission in broadband optical networks. Unlike the Internet, SDH networks are strictly planned; rings, meshes, stars, or tree-branches topologies are designed to connect their basic elements. In spite of that, we have found that the SDH network operated by Telefonica in Spain shares remarkable topological properties with other real complex networks empirically analyzed, such as the worldwide web network. In particular, we have found power-law scaling in the degree distribution (P(k) ~ k-γ) and properties of small world networks. Considering real planning directives that take into account geographical and technological variables, we propose an ad hoc computational model that reproduces the aforementioned topological traits observed in the Spanish SDH network.

IMPROVED CLUSTERING THROUGH HETEROGENEITY IN PREFERENTIAL ATTACHMENT NETWORKS

In this paper we present a study of the influence of heterogeneity on the clustering of preferential attachment networks. The study is performed by the numerical analysis of the threshold preferential attachment model, a generalization of the Barabasi—Albert model to heterogeneous complex networks. Heterogeneous networks are characterized by the existence of intrinsic properties of the nodes which induce specific affinities in their interactions. We analyze the influence of the affinity parameters on the distribution of degree-averaged clustering coefficients of the threshold model. We show that the introduction of heterogeneity increases the inverse correlation between clustering and connectivity of the nodes, inducing a power-law scaling in the clustering distribution. We also show that a higher level of heterogeneity increases the overall clustering coefficients irrespective of the node degrees. These results exhibit a better agreement of the extended model with the empirical observations of clustering in real networks.

Complexity in Spanish optical fiber and SDH transport networks

Complex networks are important instances of technology-related complex systems. In this work we apply tools from complexity science to characterise two Telefonica Espana transport network systems: the optical fiber network and the SDH transport network. We compare both cases and derive its most important properties. Remarkably, our results show that in both cases several features of heterogeneous, hierarchical complex networks arise.

TOPOLOGICAL ANALYSIS OF COMPLEX OPTICAL TRANSPORT NETWORKS

SDH (Synchronous Digital Hierarchy) is the standard technology for information transmission in broadband optical networks. Unlike the Internet, SDH networks are strictly planned — rings, meshes, stars or tree-branches topologies are designed to connect their basic elements. In this work we show that the SDH network operated by Telefonica in Spain presents a power-law scaling in the degree distribution (P(k) ~ k-γ) both at the national and provincial levels. The empirically obtained scaling exponents γ are consistent with those observed in other heterogeneous complex networks. The Spanish SDH network also displays small world properties with a high clustering and short path length similar to the Internet routers network. The province subnetworks experience similar traits with regards to such properties. Considering factors such as network design policies, user demand, geographical location and types of equipment, we propose an ad hoc computational model in order to reproduce these topological properties.

Community Structure in a Soil Porous System

Abstract Soil is well recognized as a highly complex system. The interaction and coupled physical, chemical, and biological processes and phenomena occurring in the soil environment at different spatial and temporal scales are the main reasons for such complexity. There is a need for appropriate methodologies to characterize soil porous systems with an interdisciplinary character. Four different real soil samples, presenting different textures, have been modeled as heterogeneous complex networks, applying a model known as the heterogeneous preferential attachment. An analytical study of the degree distributions in the soil model shows a multiscaling behavior in the connectivity degrees, leaving an empirically testable signature of heterogeneity in the topology of soil pore networks. We also show that the power-law scaling in the degree distribution is a robust trait of the soil model. Last, the detection of spatial pore communities, as densely connected groups with only sparser connections between them, has been studied for the first time in these soil networks. Our results show that the presence of these communities depends on the parameter values used to construct the network. These findings could contribute to understanding the mechanisms of the diffusion phenomena in soils, such as gas and water diffusion, development and dynamics of microorganisms, among others.

On the topology of optical transport networks

Synchronous Digital Hierarchy (SDH) is the standard technology for information transmission in broadband optical networks. Unlike systems with unplanned growth, such as those of natural origin or the Internet network, the SDH systems are strictly planned as rings, meshes, stars or tree-branches structures designed to connect different equipments. In spite of that, we have found that the SDH network operated by Telef?nica in Spain shares remarkable topological properties with other real complex networks as a product of its evolution since 1992. In fact, we have found power-law scaling in the degree distribution (N?P(k) = k??) and small-world networks properties. The complexity found in SDH systems was reproduced by two models of complex networks, one of them considers real planning directives that take into account geographical and technological variables and the other one is based in the compatibility among SDH equipments.

EVOLUTION OF HETEROGENEOUS NETWORKS UNDER PREFERENTIAL ATTACHMENT

In this paper, we present results concerning a natural extension of the class of heterogeneous preferential attachment models, a generalization of the Barabasi–Albert model to heterogeneous networks. In this extended class, the network nodes enjoy a nonzero attractiveness even when their connectivity degrees are zero. We analytically show that the degree densities of models in the extended class exhibit a richer scaling behavior than their homogeneous counterparts, and that power-law scaling in their degree distribution is robust in the presence of the offset in the attachment kernel.