Controlling edge dynamics in complex networks

The Internet has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus infections and find the average lifetime and persistence of viral strains on the Internet. We define a dynamical model for the spreading of infections on scale-free networks, finding the absence of an epidemic threshold and its associated critical behavior. This new epidemiological framework rationalizes data of computer viruses and could help in the understanding of other spreading phenomena on communication and social networks.

We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

Network analysis has been applied widely, providing a unifying language to describe disparate systems ranging from social interactions to power grids. It has recently been used in molecular biology, but so far the resulting networks have only been analysed statically. Here we present the dynamics of a biological network on a genomic scale, by integrating transcriptional regulatory information and gene-expression data for multiple conditions in Saccharomyces cerevisiae. We develop an approach for the statistical analysis of network dynamics, called SANDY, combining well-known global topological measures, local motifs and newly derived statistics. We uncover large changes in underlying network architecture that are unexpected given current viewpoints and random simulations. In response to diverse stimuli, transcription factors alter their interactions to varying degrees, thereby rewiring the network. A few transcription factors serve as permanent hubs, but most act transiently only during certain conditions. By studying sub-network structures, we show that environmental responses facilitate fast signal propagation (for example, with short regulatory cascades), whereas the cell cycle and sporulation direct temporal progression through multiple stages (for example, with highly inter-connected transcription factors). Indeed, to drive the latter processes forward, phase-specific transcription factors inter-regulate serially, and ubiquitously active transcription factors layer above them in a two-tiered hierarchy. We anticipate that many of the concepts presented here--particularly the large-scale topological changes and hub transience--will apply to other biological networks, including complex sub-systems in higher eukaryotes.