Sergi Valverde

Scale-free networks from optimal design

A large number of complex networks, both natural and artificial, share the presence of highly heterogeneous, scale-free degree distributions. A few mechanisms for the emergence of such patterns have been suggested, optimization not being one of them. In this letter we present the first evidence for the emergence of scaling (and the presence of small-world behavior) in software architecture graphs from a well-defined local optimization process. Although the rules that define the strategies involved in software engineering should lead to a tree-like structure, the final net is scale-free, perhaps reflecting the presence of conflicting constraints unavoidable in a multidimensional optimization process. The consequences for other complex networks are outlined.

TOPOLOGICAL VULNERABILITY OF THE EUROPEAN POWER GRID UNDER ERRORS AND ATTACKS

We present an analysis of the topological structure and static tolerance to errors and attacks of the September 2003 actualization of the Union for the Coordination of Transport of Electricity (UCTE) power grid, involving thirty-three different networks. Though every power grid studied has exponential degree distribution and most of them lack typical small-world topology, they display patterns of reaction to node loss similar to those observed in scale-free networks. We have found that the node removal behavior can be logarithmically related to the power grid size. This logarithmic behavior would suggest that, though size favors fragility, growth can reduce it. We conclude that, with the ever-growing demand for power and reliability, actual planning strategies to increase transmission systems would have to take into account this relative increase in vulnerability with size, in order to facilitate and improve the power grid design and functioning.

Robustness of the European power grids under intentional attack

The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it becomes extremely fragile as well, when unexpected, usually minimal, failures turn into unknown dynamical behaviours leading, for example, to sudden and massive blackouts. Here we explore the fragility of the European power grid under the effect of selective node removal. A mean field analysis of fragility against attacks is presented together with the observed patterns. Deviations from the theoretical conditions for network percolation (and fragmentation) under attacks are analysed and correlated with non topological reliability measures.

Statistical structure of host-phage interactions

Interactions between bacteria and the viruses that infect them (i.e., phages) have profound effects on biological processes, but despite their importance, little is known on the general structure of infection and resistance between most phages and bacteria. For example, are bacteria–phage communities characterized by complex patterns of overlapping exploitation networks, do they conform to a more ordered general pattern across all communities, or are they idiosyncratic and hard to predict from one ecosystem to the next? To answer these questions, we collect and present a detailed metaanalysis of 38 laboratory-verified studies of host–phage interactions representing almost 12,000 distinct experimental infection assays across a broad spectrum of taxa, habitat, and mode of selection. In so doing, we present evidence that currently available host–phage infection networks are statistically different from random networks and that they possess a characteristic nested structure. This nested structure is typified by the finding that hard to infect bacteria are infected by generalist phages (and not specialist phages) and that easy to infect bacteria are infected by generalist and specialist phages. Moreover, we find that currently available host–phage infection networks do not typically possess a modular structure. We explore possible underlying mechanisms and significance of the observed nested host–phage interaction structure. In addition, given that most of the available host–phage infection networks examined here are composed of taxa separated by short phylogenetic distances, we propose that the lack of modularity is a scale-dependent effect, and then, we describe experimental studies to test whether modular patterns exist at macroevolutionary scales.

Information transfer and phase transitions in a model of internet traffic

In a recent study, Ohira and Sawatari presented a simple model of computer network traffic dynamics. These authors showed that a phase transition point is present separating the low-traffic phase with no congestion from the congestion phase as the packet creation rate increases. We further investigate this model by relaxing the network topology using a random location of routers. It is shown that the model exhibits nontrivial scaling properties close to the critical point, which reproduce some of the observed real Internet features. At criticality the net shows maximum information tranfer and efficiency. It is shown that some of the key properties of this model are shared by highway traffic models, as previously conjectured by some authors. The relevance to Internet dynamics and to the performance of parallel arrays of processors is discussed.

Phage-bacteria infection networks.

Phage and their bacterial hosts are the most abundant and genetically diverse group of organisms on the planet. Given their dominance, it is no wonder that many recent studies have found that phage-bacteria interactions strongly influence global biogeochemical cycles, incidence of human diseases, productivity of industrial microbial commodities, and patterns of microbial genome diversity. Unfortunately, given the extreme diversity and complexity of microbial communities, traditional analyses fail to characterize interaction patterns and underlying processes. Here, we review emerging systems approaches that combine empirical data with rigorous theoretical analysis to study phage-bacterial interactions as networks rather than as coupled interactions in isolation.

Topology and evolution of technology innovation networks.

The web of relations linking technological innovation can be fairly described in terms of patent citations. The resulting patent citation network provides a picture of the large-scale organization of innovations and its time evolution. Here we study the patterns of change of patents registered by the U.S. Patent and Trademark Office. We show that the scaling behavior exhibited by this network is consistent with a preferential attachment mechanism together with a Weibull-shaped aging term. Such an attachment kernel is shared by scientific citation networks, thus indicating a universal type of mechanism linking ideas and designs and their evolution. The implications for evolutionary theory of innovation are discussed.

Spontaneous emergence of modularity in cellular networks.

Modularity is known to be one of the most relevant characteristics of biological systems and appears to be present at multiple scales. Given its adaptive potential, it is often assumed to be the target of selective pressures. Under such interpretation, selection would be actively favouring the formation of modular structures, which would specialize in different functions. Here we show that, within the context of cellular networks, no such selection pressure is needed to obtain modularity. Instead, the intrinsic dynamics of network growth by duplication and diversification is able to generate it for free and explain the statistical features exhibited by small subgraphs. The implications for the evolution and evolvability of both biological and technological systems are discussed.

Multi-scale structure and geographic drivers of cross-infection within marine bacteria and phages

Bacteriophages are the most abundant biological life forms on Earth. However, relatively little is known regarding which bacteriophages infect and exploit which bacteria. A recent meta-analysis showed that empirically measured phage-bacteria infection networks are often significantly nested, on average, and not modular. A perfectly nested network is one in which phages can be ordered from specialist to generalist such that the host range of a given phage is a subset of the host range of the subsequent phage in the ordering. The same meta-analysis hypothesized that modularity, in which groups of phages specialize on distinct groups of hosts, should emerge at larger geographic and/or taxonomic scales. In this paper, we evaluate the largest known phage-bacteria interaction data set, representing the interaction of 215 phage types with 286 host types sampled from geographically separated sites in the Atlantic Ocean. We find that this interaction network is highly modular. In addition, some of the modules identified in this data set are nested or contain submodules, indicating the presence of multi-scale structure, as hypothesized in the earlier meta-analysis. We examine the role of geography in driving these patterns and find evidence that the host range of phages and the phage permissibility of bacteria is driven, in part, by geographic separation. We conclude by discussing approaches to disentangle the roles of ecology and evolution in driving complex patterns of interaction between phages and bacteria.

Self-organized critical traffic in parallel computer networks

In a recent paper, we analysed the dynamics of traffic flow in a simple, square lattice architecture. It was shown that a phase transition takes place between a free and a congested phase. The transition point was shown to exhibit optimal information transfer and wide fluctuations in time, with scale-free properties. In this paper, we further extend our analysis by considering a generalization of the previous model in which the rate of packet emission is regulated by the local congestion perceived by each node. As a result of the feedback between traffic congestion and packet release, the system is poised at criticality. Many well-known statistical features displayed by Internet traffic are recovered from our model in a natural way.