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

Structural Inference of Hierarchies in Networks

One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of organization in the network. Here, we give a precise definition of hierarchical structure, give a generic model for generating arbitrary hierarchical structure in a random graph, and describe a statistically principled way to learn the set of hierarchical features that most plausibly explain a particular real-world network. By applying this approach to two example networks, we demonstrate its advantages for the interpretation of network data, the annotation of graphs with edge, vertex and community properties, and the generation of generic null models for further hypothesis testing.Comment: 8 pages, 8 figure

Robust Detection of Hierarchical Communities from Escherichia coli Gene Expression Data

Determining the functional structure of biological networks is a central goal of systems biology. One approach is to analyze gene expression data to infer a network of gene interactions on the basis of their correlated responses to environmental and genetic perturbations. The inferred network can then be analyzed to identify functional communities. However, commonly used algorithms can yield unreliable results due to experimental noise, algorithmic stochasticity, and the influence of arbitrarily chosen parameter values. Furthermore, the results obtained typically provide only a simplistic view of the network partitioned into disjoint communities and provide no information of the relationship between communities. Here, we present methods to robustly detect coregulated and functionally enriched gene communities and demonstrate their application and validity for Escherichia coli gene expression data. Applying a recently developed community detection algorithm to the network of interactions identified with the context likelihood of relatedness (CLR) method, we show that a hierarchy of network communities can be identified. These communities significantly enrich for gene ontology (GO) terms, consistent with them representing biologically meaningful groups. Further, analysis of the most significantly enriched communities identified several candidate new regulatory interactions. The robustness of our methods is demonstrated by showing that a core set of functional communities is reliably found when artificial noise, modeling experimental noise, is added to the data. We find that noise mainly acts conservatively, increasing the relatedness required for a network link to be reliably assigned and decreasing the size of the core communities, rather than causing association of genes into new communities.Comment: Due to appear in PLoS Computational Biology. Supplementary Figure S1 was not uploaded but is available by contacting the author. 27 pages, 5 figures, 15 supplementary file

A Systematic Analysis of Community Detection in Complex Networks

Numerous techniques have been proposed by researchers to uncover the hidden patterns of real-world complex networks. Finding a hidden community is one of the crucial tasks for community detection in complex networks. Despite the presence of multiple methods for community detection, identification of the best performing method over different complex networks is still an open research question. In this article, we analyzed eight state-of-the-art community detection algorithms on nine complex networks of varying sizes covering various domains including animal, biomedical, terrorist, social, and human contacts. The objective of this article is to identify the best performing algorithm for community detection in real-world complex networks of various sizes and from different domains. The obtained results over 100 iterations demonstrated that the multi-scale method has outperformed the other techniques in terms of accuracy. Multi-scale method achieved 0.458 average value of modularity metric whereas multiple screening resolution, unfolding fast, greedy, multi-resolution, local fitness optimization, sparse Geosocial community detection algorithm, and spectral clustering, respectively obtained the modularity values 0.455, 0.441, 0.436, 0.421, 0.368, 0.341, and 0.340.

Multi-objective NSGA-II based community detection using dynamical evolution social network

Community detection is becoming a highly demanded topic in social networking-based applications. It involves finding the maximum intraconnected and minimum inter-connected sub-graphs in given social networks. Many approaches have been developed for community’s detection and less of them have focused on the dynamical aspect of the social network. The decision of the community has to consider the pattern of changes in the social network and to be smooth enough. This is to enable smooth operation for other community detection dependent application. Unlike dynamical community detection Algorithms, this article presents a non-dominated aware searching Algorithm designated as non-dominated sorting based community detection with dynamical awareness (NDS-CD-DA). The Algorithm uses a non-dominated sorting genetic algorithm NSGA-II with two objectives: modularity and normalized mutual information (NMI). Experimental results on synthetic networks and real-world social network datasets have been compared with classical genetic with a single objective and has been shown to provide superiority in terms of the domination as well as the convergence. NDS-CD-DA has accomplished a domination percentage of 100% over dynamic evolutionary community searching DECS for almost all iterations

Hierarchical community structure in networks

Modular and hierarchical structures are pervasive in real-world complex systems. A great deal of effort has gone into trying to detect and study these structures. Important theoretical advances in the detection of modular, or "community", structures have included identifying fundamental limits of detectability by formally defining community structure using probabilistic generative models. Detecting hierarchical community structure introduces additional challenges alongside those inherited from community detection. Here we present a theoretical study on hierarchical community structure in networks, which has thus far not received the same rigorous attention. We address the following questions: 1)~How should we define a valid hierarchy of communities? 2)~How should we determine if a hierarchical structure exists in a network? and 3)~how can we detect hierarchical structure efficiently? We approach these questions by introducing a definition of hierarchy based on the concept of stochastic externally equitable partitions and their relation to probabilistic models, such as the popular stochastic block model. We enumerate the challenges involved in detecting hierarchies and, by studying the spectral properties of hierarchical structure, present an efficient and principled method for detecting them.Comment: 22 pages, 12 figure

Passenger Flows in the Metropolitan Seoul Public Transportation: Maximum Spanning Tree and Community Detection

학위논문 (석사)-- 서울대학교 대학원 : 물리·천문학부(물리학전공), 2013. 2. 최무영.본 논문에서는 서울 수도권의 대중교통 시스템에서의 승객 흐름을 최대신장나무와 지역사회 찾기를 통해 살펴보았다. 대중교통 수단인 버스와 지하철은 사람들의 주된 교통 수단으로 제공된다. 사람들의 움직임의 특성은 승객 흐름 데이터를 통해 분석할 수 있다. 이 논문에서는 역을 출발역과 도착역으로 나누어 승객흐름의 최대신장나무를 구성하였다. 최대신장나무에서 출발역과 도착역의 연결 수 분포는 거듭제곱 법칙을 따르며 시간대에 따라 지수는 달랐다. 이 논문에서는 또한 서울 수도권의 지역사회 구조를 연구하였다. 버스와 지하철 역을 사각 격자로 대충 갈기 한 뒤 모듈럴리티 최대화를 도입하여 사각 영역으로 표현되는 노드들로 구분된 지역사회를 구하였다. 단일 연결 합치기 방법과 분할 밀도 최대화를 통해 구분된 링크들의 지역사회를 구하여 중첩된 지역사회를 발견하였다. 한 지역사회 안의 노드 수와 링크 수의 분포는 역시 거듭제곱 법칙을 따른다. 이 지역사회들은 사람들의 실제 이동 자료를 통해 찾았다는 측면에서 실제 서울 수도권의 지역사회 특성을 보여준다고 생각할 수 있다.In this thesis, passenger flow of Metropolitan Seoul public transportation system is examined through maximum spanning tree and community detection. The public transportation system, consisting bus and subway, provides major transportation modes to the people. The characteristic of movement of people can be analyzed by the passenger flow data of public transportation system. We divide one station by departure station and arrival station and construct maximum spanning tree of the passenger flow. The degree distribution of the departure stations and arrival stations in the maximum spanning tree follows power law with different exponent according to the time zones. We also investigate the community structure of Metropolitan Seoul. The bus and subway stations are coarse grained by square grid and the modularity maximization method using simulated annealing is employed first to find disjoint node(square area) communities. The disjoint link community, using single-linkage agglomerate method and partition density maximization, is also found to reveal overlapped communities. The distribution of number of links and nodes per community in the disjoint link community also follows power law distribution. These communities can be regarded showing real community character of Metropolitan Seoul in the sense of the lexical meaning of community.1 Introduction 1 2 Maximum Spanning Trees of Passenger Flow 4 2.1 Introduction 4 2.2 Method 5 2.3 Results 6 3 Community Detection 14 3.1 Introduction 14 3.2 Method 16 3.2.1 Modularity maximization by simulated annealing 16 3.2.2 Overlapped community detection: Disjoint link community 17 3.3 Results 18 3.3.1 Modularity maximization by simulated annealing 18 3.3.2 Overlapped community detection: Disjoint link community 19 4 Summary 27Maste