Identifying network communities with a high resolution

Community structure is an important property of complex networks. An automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a quantity called modularity (Q). However, the problem of modularity optimization is NP-hard, and the existing approaches often suffer from prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing Q will have a resolution limit, i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm, Qcut, which combines spectral graph partitioning and local search to optimize Q. Using both synthetic and real networks, we show that Qcut can find higher modularities and is more scalable than the existing algorithms. Furthermore, using Qcut as an essential component, we propose a recursive algorithm, HQcut, to solve the resolution limit problem. We show that HQcut can successfully detect communities at a much finer scale and with a higher accuracy than the existing algorithms. Finally, we apply Qcut and HQcut to study a protein-protein interaction network, and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetectable.Comment: 14 pages, 5 figures. 1 supplemental file at http://cic.cs.wustl.edu/qcut/supplemental.pd

Evaluating Local Community Methods in Networks

We present a new benchmarking procedure that is unambiguous and specific to local community-finding methods, allowing one to compare the accuracy of various methods. We apply this to new and existing algorithms. A simple class of synthetic benchmark networks is also developed, capable of testing properties specific to these local methods.Comment: 8 pages, 9 figures, code included with sourc

Evaluation de l’effet repulsif d’extraits de neem (Azadirachta indica A. Juss., 1830) sur le charançon de la patate douce (Cylas puncticollis Boheman, 1833) en condition de laboratoire a Korhogo, nord de la Cote d’Ivoire

Une stratégie de gestion intégrée des insectes nuisibles à la culture de la patate douce a été élaborée pour réduire les pertes dues à ceux-ci. Ainsi, les propriétés répulsives des extraits de feuilles et d’amandes de neem ont été évaluées sur Cylas puncticollis, un charançon de la patate douce. Pour ce faire, quatre concentrations d’extraits ont été préparées à raison de quatre répétitions par concentration. Le test a consisté à la détermination du pourcentage de charançons présents dans la zone traitée. Chacune des concentrations d’extraits a été appliquée sur la moitié d’un papier buvard placé dans une boite de Pétri de 9 cm de diamètre et sur lequel 10 charançons ont été posés. Les effets répulsifs des extraits ont été comparés à ceux d’un insecticide chimique et l’eau distillée. Le test avec 20 cL/L d’extraits de feuilles a causé 85 % de répulsion contre 45 % pour les amandes à 25 g/L. Les extraits ont significativement causé plus de répulsion que l’eau distillée et l’insecticide chimique. Les tests ont révélé un potentiel plus répulsif des extraits de feuilles comparé à celui des amandes. Les extraits de neem pourraient constituer une alternative crédible à la lutte chimique pour la protection de la patate douce contre ce charançon. English title: Evaluation of the repellent effect of neem extracts (Azadirachta indica A. Juss., 1830) on the sweet potato weevil (Cylas puncticollis Boheman, 1833) under laboratory conditions in Korhogo, northern Côte d’Ivoire Abstract An integrated pest management strategy for sweet potatoes has been developed to reduce pest losses. Thus, the repellent properties of neem leaf and kernel extracts were evaluated on Cylas puncticollis, a sweet potato weevil. For this purpose, four concentrations of extracts were prepared with four replicates per concentration. The test consisted of determining the percentage of weevils in the treated area. Each of the extract concentrations was applied to half of a blotting paper placed in 9 cm diameter Petri dishes on which 10 weevils were placed. The repellent effects of the extracts were compared to those of a chemical insecticide and distilled water. Test with 20 cL/L leaf extract caused 85% repellence compared to 45% for almonds at 25 g/L. Compared to the chemical insecticide and distilled water, the extracts caused significantly more repellence. The tests revealed a higher repellent potential of the leaf extracts compared to those of almonds. Neem extracts could be a credible alternative to chemical control for the protection of sweet potato against this weevil. Keywords: Neem extracts, Repellent effect, Sweet potato, Cylas puncticolli

Local multiresolution order in community detection

Community detection algorithms attempt to find the best clusters of nodes in an arbitrary complex network. Multi-scale ("multiresolution") community detection extends the problem to identify the best network scale(s) for these clusters. The latter task is generally accomplished by analyzing community stability simultaneously for all clusters in the network. In the current work, we extend this general approach to define local multiresolution methods, which enable the extraction of well-defined local communities even if the global community structure is vaguely defined in an average sense. Toward this end, we propose measures analogous to variation of information and normalized mutual information that are used to quantitatively identify the best resolution(s) at the community level based on correlations between clusters in independently-solved systems. We demonstrate our method on two constructed networks as well as a real network and draw inferences about local community strength. Our approach is independent of the applied community detection algorithm save for the inherent requirement that the method be able to identify communities across different network scales, with appropriate changes to account for how different resolutions are evaluated or defined in a particular community detection method. It should, in principle, easily adapt to alternative community comparison measures.Comment: 19 pages, 11 figure

Enhance the Efficiency of Heuristic Algorithm for Maximizing Modularity Q

Modularity Q is an important function for identifying community structure in complex networks. In this paper, we prove that the modularity maximization problem is equivalent to a nonconvex quadratic programming problem. This result provide us a simple way to improve the efficiency of heuristic algorithms for maximizing modularity Q. Many numerical results demonstrate that it is very effective.Comment: 9 pages, 3 figure

Spatial correlations in attribute communities

Community detection is an important tool for exploring and classifying the properties of large complex networks and should be of great help for spatial networks. Indeed, in addition to their location, nodes in spatial networks can have attributes such as the language for individuals, or any other socio-economical feature that we would like to identify in communities. We discuss in this paper a crucial aspect which was not considered in previous studies which is the possible existence of correlations between space and attributes. Introducing a simple toy model in which both space and node attributes are considered, we discuss the effect of space-attribute correlations on the results of various community detection methods proposed for spatial networks in this paper and in previous studies. When space is irrelevant, our model is equivalent to the stochastic block model which has been shown to display a detectability-non detectability transition. In the regime where space dominates the link formation process, most methods can fail to recover the communities, an effect which is particularly marked when space-attributes correlations are strong. In this latter case, community detection methods which remove the spatial component of the network can miss a large part of the community structure and can lead to incorrect results.Comment: 10 pages and 7 figure

Cascading Dynamics in Modular Networks

In this paper we study a simple cascading process in a structured heterogeneous population, namely, a network composed of two loosely coupled communities. We demonstrate that under certain conditions the cascading dynamics in such a network has a two--tiered structure that characterizes activity spreading at different rates in the communities. We study the dynamics of the model using both simulations and an analytical approach based on annealed approximation, and obtain good agreement between the two. Our results suggest that network modularity might have implications in various applications, such as epidemiology and viral marketing.Comment: 5 pages, 4 figure

Comparing community structure identification

We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as appears in JSTA

Consensus clustering in complex networks

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on the specific random seeds, initial conditions and tie-break rules adopted for their execution. Consensus clustering is used in data analysis to generate stable results out of a set of partitions delivered by stochastic methods. Here we show that consensus clustering can be combined with any existing method in a self-consistent way, enhancing considerably both the stability and the accuracy of the resulting partitions. This framework is also particularly suitable to monitor the evolution of community structure in temporal networks. An application of consensus clustering to a large citation network of physics papers demonstrates its capability to keep track of the birth, death and diversification of topics.Comment: 11 pages, 12 figures. Published in Scientific Report

Characterizing the community structure of complex networks

Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has been so far devoted to the investigation of communities in real networks. We present a systematic empirical analysis of the statistical properties of communities in large information, communication, technological, biological, and social networks. We find that the mesoscopic organization of networks of the same category is remarkably similar. This is reflected in several characteristics of community structure, which can be used as ``fingerprints'' of specific network categories. While community size distributions are always broad, certain categories of networks consist mainly of tree-like communities, while others have denser modules. Average path lengths within communities initially grow logarithmically with community size, but the growth saturates or slows down for communities larger than a characteristic size. This behaviour is related to the presence of hubs within communities, whose roles differ across categories. Also the community embeddedness of nodes, measured in terms of the fraction of links within their communities, has a characteristic distribution for each category. Our findings are verified by the use of two fundamentally different community detection methods.Comment: 15 pages, 20 figures, 4 table