The inhomogeneous evolution of subgraphs and cycles in complex networks

Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains unchanged, while the density of others increase at a rate that is determined by the network's degree distribution and clustering properties. This inhomogeneous evolution process, supported by direct measurements on several real networks, leads to systematic shifts in the overall subgraph spectrum and to an inevitable overrepresentation of some subgraphs and cycles.Comment: 4 pages, 4 figures, submitted to Phys. Rev.

Flexible construction of hierarchical scale-free networks with general exponent

Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model which reproduces the main experimental properties observed in real networks: scale-free of degree distribution $P(k)$ (frequency of the nodes that are connected to $k$ other nodes decays as a power-law $P(k)\sim k^{-\gamma}$) and power-law scaling of the clustering coefficient $C(k)\sim k^{-1}$. The major novelties of our model can be summarized as follows: {\it (a)} The model generates networks with scale-free distribution for the degree of nodes with general exponent $\gamma > 2$, and arbitrarily close to any specified value, being able to reproduce most of the observed hierarchical scale-free topologies. In contrast, previous models can not obtain values of $\gamma > 2.58$. {\it (b)} Our model has structural flexibility because {\it (i)} it can incorporate various types of basic building blocks (e.g., triangles, tetrahedrons and, in general, fully connected clusters of $n$ nodes) and {\it (ii)} it allows a large variety of configurations (i.e., the model can use more than $n-1$ copies of basic blocks of $n$ nodes). The structural features of our proposed model might lead to a better understanding of architectures of biological and non-biological networks.Comment: RevTeX, 5 pages, 4 figure

Rich-Club Phenomenon in the Interactome of P. falciparum—Artifact or Signature of a Parasitic Life Style?

Recent advances have provided a first experimental protein interaction map of the human malaria parasite P. falciparum, which appears to be remotely related to interactomes of other eukaryotes. Here, we present a comparative topological analysis of this experimentally determined web with a network of conserved interactions between proteins in S. cerevisiae, C. elegans and D. melanogaster that have an ortholog in Plasmodium. Focusing on experimental interactions, we find a significant presence of a “rich-club,” a topological characteristic that features an “oligarchy” of highly connected proteins being intertwined with one another. In complete contrast, the network of interologs and particularly the web of evolutionary-conserved interactions in P. falciparum lack this feature. This observation prompts the question of whether this result points to a topological signature of the parasite's biology, since experimentally obtained interactions widely cover parasite-specific functions. Significantly, hub proteins that appear in such an oligarchy revolve around invasion functions, shaping an island of parasite-specific activities in a sea of evolutionary inherited interactions. This presence of a biologically unprecedented network feature in the human malaria parasite might be an artifact of the quality and the methods to obtain interaction data in this organism. Yet, the observation that rich-club proteins have distinctive and statistically significant functions that revolve around parasite-specific activities point to a topological signature of a parasitic life style

Subgraph Centrality in Complex Networks

We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network motifs. We show that the subgraph centrality (SC) can be obtained mathematically from the spectra of the adjacency matrix of the network. This measure is better able to discriminate the nodes of a network than alternate measures such as degree, closeness, betweenness and eigenvector centralities. We study eight real-world networks for which SC displays useful and desirable properties, such as clear ranking of nodes and scale-free characteristics. Compared with the number of links per node, the ranking introduced by SC (for the nodes in the protein interaction network of S. cereviciae) is more highly correlated with the lethality of individual proteins removed from the proteome.Comment: 29 pages, 4 figures, 2 table

Cycle-centrality in complex networks

Networks are versatile representations of the interactions between entities in complex systems. Cycles on such networks represent feedback processes which play a central role in system dynamics. In this work, we introduce a measure of the importance of any individual cycle, as the fraction of the total information flow of the network passing through the cycle. This measure is computationally cheap, numerically well-conditioned, induces a centrality measure on arbitrary subgraphs and reduces to the eigenvector centrality on vertices. We demonstrate that this measure accurately reflects the impact of events on strategic ensembles of economic sectors, notably in the US economy. As a second example, we show that in the protein-interaction network of the plant Arabidopsis thaliana, a model based on cycle-centrality better accounts for pathogen activity than the state-of-art one. This translates into pathogen-targeted-proteins being concentrated in a small number of triads with high cycle-centrality. Algorithms for computing the centrality of cycles and subgraphs are available for download

Influence of degree correlations on network structure and stability in protein-protein interaction networks

<p>Abstract</p> <p>Background</p> <p>The existence of negative correlations between degrees of interacting proteins is being discussed since such negative degree correlations were found for the large-scale <it>yeast </it>protein-protein interaction (PPI) network of Ito et al. More recent studies observed no such negative correlations for high-confidence interaction sets. In this article, we analyzed a range of experimentally derived interaction networks to understand the role and prevalence of degree correlations in PPI networks. We investigated how degree correlations influence the structure of networks and their tolerance against perturbations such as the targeted deletion of hubs.</p> <p>Results</p> <p>For each PPI network, we simulated uncorrelated, positively and negatively correlated reference networks. Here, a simple model was developed which can create different types of degree correlations in a network without changing the degree distribution. Differences in static properties associated with degree correlations were compared by analyzing the network characteristics of the original PPI and reference networks. Dynamics were compared by simulating the effect of a selective deletion of hubs in all networks.</p> <p>Conclusion</p> <p>Considerable differences between the network types were found for the number of components in the original networks. Negatively correlated networks are fragmented into significantly less components than observed for positively correlated networks. On the other hand, the selective deletion of hubs showed an increased structural tolerance to these deletions for the positively correlated networks. This results in a lower rate of interaction loss in these networks compared to the negatively correlated networks and a decreased disintegration rate. Interestingly, real PPI networks are most similar to the randomly correlated references with respect to all properties analyzed. Thus, although structural properties of networks can be modified considerably by degree correlations, biological PPI networks do not actually seem to make use of this possibility.</p

Does Collocation Inform the Impact of Collaboration?

Background It has been shown that large interdisciplinary teams working across geography are more likely to be impactful. We asked whether the physical proximity of collaborators remained a strong predictor of the scientific impact of their research as measured by citations of the resulting publications. Methodology/Principal Findings Articles published by Harvard investigators from 1993 to 2003 with at least two authors were identified in the domain of biomedical science. Each collaboration was geocoded to the precise three-dimensional location of its authors. Physical distances between any two coauthors were calculated and associated with corresponding citations. Relationship between distance of coauthors and citations for four author relationships (first-last, first-middle, last-middle, and middle-middle) were investigated at different spatial scales. At all sizes of collaborations (from two authors to dozens of authors), geographical proximity between first and last author is highly informative of impact at the microscale (i.e. within building) and beyond. The mean citation for first-last author relationship decreased as the distance between them increased in less than one km range as well as in the three categorized ranges (in the same building, same city, or different city). Such a trend was not seen in other three author relationships. Conclusions/Significance Despite the positive impact of emerging communication technologies on scientific research, our results provide striking evidence for the role of physical proximity as a predictor of the impact of collaborations.Ewing Marion Kauffman FoundationHarvard University. Office of the Provost (1992-

The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation

A minimum dominating set for a digraph (directed graph) is a smallest set of vertices such that each vertex either belongs to this set or has at least one parent vertex in this set. We solve this hard combinatorial optimization problem approximately by a local algorithm of generalized leaf removal and by a message-passing algorithm of belief propagation. These algorithms can construct near-optimal dominating sets or even exact minimum dominating sets for random digraphs and also for real-world digraph instances. We further develop a core percolation theory and a replica-symmetric spin glass theory for this problem. Our algorithmic and theoretical results may facilitate applications of dominating sets to various network problems involving directed interactions.Comment: 11 pages, 3 figures in EPS forma