A Method to Find Community Structures Based on Information Centrality

Community structures are an important feature of many social, biological and technological networks. Here we study a variation on the method for detecting such communities proposed by Girvan and Newman and based on the idea of using centrality measures to define the community boundaries (M. Girvan and M. E. J. Newman, Community structure in social and biological networks Proc. Natl. Acad. Sci. USA 99, 7821-7826 (2002)). We develop an algorithm of hierarchical clustering that consists in finding and removing iteratively the edge with the highest information centrality. We test the algorithm on computer generated and real-world networks whose community structure is already known or has been studied by means of other methods. We show that our algorithm, although it runs to completion in a time O(n^4), is very effective especially when the communities are very mixed and hardly detectable by the other methods.Comment: 13 pages, 13 figures. Final version accepted for publication in Physical Review

Condensation phase transition in nonlinear fitness networks

We analyze the condensation phase transitions in out-of-equilibrium complex networks in a unifying framework which includes the nonlinear model and the fitness model as its appropriate limits. We show a novel phase structure which depends on both the fitness parameter and the nonlinear exponent. The occurrence of the condensation phase transitions in the dynamical evolution of the network is demonstrated by using Bianconi-Barabasi method. We find that the nonlinear and the fitness preferential attachment mechanisms play important roles in formation of an interesting phase structure.Comment: 6 pages, 5 figure

Information dynamics algorithm for detecting communities in networks

The problem of community detection is relevant in many scientific disciplines, from social science to statistical physics. Given the impact of community detection in many areas, such as psychology and social sciences, we have addressed the issue of modifying existing well performing algorithms by incorporating elements of the domain application fields, i.e. domain-inspired. We have focused on a psychology and social network - inspired approach which may be useful for further strengthening the link between social network studies and mathematics of community detection. Here we introduce a community-detection algorithm derived from the van Dongen's Markov Cluster algorithm (MCL) method by considering networks' nodes as agents capable to take decisions. In this framework we have introduced a memory factor to mimic a typical human behavior such as the oblivion effect. The method is based on information diffusion and it includes a non-linear processing phase. We test our method on two classical community benchmark and on computer generated networks with known community structure. Our approach has three important features: the capacity of detecting overlapping communities, the capability of identifying communities from an individual point of view and the fine tuning the community detectability with respect to prior knowledge of the data. Finally we discuss how to use a Shannon entropy measure for parameter estimation in complex networks.Comment: Submitted to "Communication in Nonlinear Science and Numerical Simulation

Immunization of Susceptible-Infected Model on Scale-Free networks

In this paper, we investigate two major immunization strategies, random immunization and targeted immunization, of the susceptible-infected (SI) Model on the Barab\'{a}si-Albert (BA) networks. For the heterogenous structure, the random strategy is quite ineffective if the vaccinated proportion is quite small, while the targeted one which prefers to vaccinate the individuals with the largest degree can sharply depress the epidemic spreading even only a small amount of population are vaccinated. The analytical solution is also obtained,which can capture the trend of velocity change versus the amount of vaccinated population.Comment: 5 pages, 4 figure

Predicting Cell Cycle Regulated Genes by Causal Interactions

The fundamental difference between classic and modern biology is that technological innovations allow to generate high-throughput data to get insights into molecular interactions on a genomic scale. These high-throughput data can be used to infer gene networks, e.g., the transcriptional regulatory or signaling network, representing a blue print of the current dynamical state of the cellular system. However, gene networks do not provide direct answers to biological questions, instead, they need to be analyzed to reveal functional information of molecular working mechanisms. In this paper we propose a new approach to analyze the transcriptional regulatory network of yeast to predict cell cycle regulated genes. The novelty of our approach is that, in contrast to all other approaches aiming to predict cell cycle regulated genes, we do not use time series data but base our analysis on the prior information of causal interactions among genes. The major purpose of the present paper is to predict cell cycle regulated genes in S. cerevisiae. Our analysis is based on the transcriptional regulatory network, representing causal interactions between genes, and a list of known periodic genes. No further data are used. Our approach utilizes the causal membership of genes and the hierarchical organization of the transcriptional regulatory network leading to two groups of periodic genes with a well defined direction of information flow. We predict genes as periodic if they appear on unique shortest paths connecting two periodic genes from different hierarchy levels. Our results demonstrate that a classical problem as the prediction of cell cycle regulated genes can be seen in a new light if the concept of a causal membership of a gene is applied consequently. This also shows that there is a wealth of information buried in the transcriptional regulatory network whose unraveling may require more elaborate concepts than it might seem at first

Hierarchical coordination of periodic genes in the cell cycle of Saccharomyces cerevisiae

<p>Abstract</p> <p>Background</p> <p>Gene networks are a representation of molecular interactions among genes or products thereof and, hence, are forming causal networks. Despite intense studies during the last years most investigations focus so far on inferential methods to reconstruct gene networks from experimental data or on their structural properties, e.g., degree distributions. Their structural analysis to gain functional insights into organizational principles of, e.g., pathways remains so far under appreciated.</p> <p>Results</p> <p>In the present paper we analyze cell cycle regulated genes in <it>S. cerevisiae</it>. Our analysis is based on the transcriptional regulatory network, representing causal interactions and not just associations or correlations between genes, and a list of known periodic genes. No further data are used. Partitioning the transcriptional regulatory network according to a graph theoretical property leads to a hierarchy in the network and, hence, in the information flow allowing to identify two groups of periodic genes. This reveals a novel conceptual interpretation of the working mechanism of the cell cycle and the genes regulated by this pathway.</p> <p>Conclusion</p> <p>Aside from the obtained results for the cell cycle of yeast our approach could be exemplary for the analysis of general pathways by exploiting the rich causal structure of inferred and/or curated gene networks including protein or signaling networks.</p

Network model of deviation from power-law distribution in complex network

Deviation from simple power law is widely observed in complex networks. We introduce a model including possible mechanisms leading to the deviation. In this model, probabilistic addition of nodes and links, as well as rewiring of links are considered. Using master equation, through theoretical calculation and numerical simulation, double power laws with one variable and one constant exponent are obtained. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011