Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks (original) (raw)

Detection of local community structures in complex dynamic networks with random walks

IET Systems Biology, 2009

Identification of interaction patterns in complex networks via community structures has gathered a lot of attention in recent research studies. Local community structures provide a better measure to understand and visualise the nature of interaction when the global knowledge of networks is unknown. Recent research on local community structures, however, lacks the feature to adjust itself in the dynamic networks and heavily depends on the source vertex position. In this study the authors propose a novel approach to identify local communities based on iterative agglomeration and local optimisation. The proposed solution has two significant improvements: (i) in each iteration, agglomeration strengthens the local community measure by selecting the best possible set of vertices, and (ii) the proposed vertex and community rank criterion are suitable for the dynamic networks where the interactions among vertices may change over time. In order to evaluate the proposed algorithm, extensive experiments and benchmarking on computer generated networks as well as real-world social and biological networks have been conducted. The experiment results reflect that the proposed algorithm can identify local communities, irrespective of the source vertex position, with more than 92% accuracy in the synthetic as well as in the real-world networks.

The stability of a graph partition: A dynamics-based framework for community detection

Recent years have seen a surge of interest in the analysis of complex networks, facilitated by the availability of relational data and the increasingly powerful computational resources that can be employed for their analysis. Naturally, the study of real-world systems leads to highly complex networks and a current challenge is to extract intelligible, simplified descriptions from the network in terms of relevant subgraphs, which can provide insight into the structure and function of the overall system. Sparked by seminal work by Newman and Girvan, an interesting line of research has been devoted to investigating modular community structure in networks, revitalising the classic problem of graph partitioning. However, modular or community structure in networks has notoriously evaded rigorous definition. The most accepted notion of community is perhaps that of a group of elements which exhibit a stronger level of interaction within themselves than with the elements outside the communit...

Coding of Markov dynamics for multiscale community detection in complex networks

Arxiv preprint arXiv:1109.6642, 2011

Abstract: The detection of community structure in complex networks is intimately related to the problem of finding a concise description of the network in terms of its modules. This notion has been recently exploited by the Map equation formalism (M. Rosvall and CT Bergstrom, PNAS, vol. 105, no. 4, pp. 1118-1123, 2008) through an information-theoretic characterization of the process of coding the transitions of a random walker inside and between communities at stationarity. However, a thorough consideration of the ...

Detecting Functional Communities in Complex Networks

2009

We consider an alternate definition of community structure that is functionally motivated. We define network community structure-based on the function the network system is intended to perform. In particular, as a specific example of this approach, we consider communities whose function is enhanced by the ability to synchronize and/or by resilience to node failures. Previous work has shown that, in many cases, the largest eigenvalue of the network's adjacency matrix controls the onset of both synchronization and percolation processes. Thus, for networks whose functional performance is dependent on these processes, we propose a method that divides a given network into communities based on maximizing a function of the largest eigenvalues of the adjacency matrices of the resulting communities. We also explore the differences between the partitions obtained by our method and the modularity approach (which is based solely on consideration of network structure). We do this for several different classes of networks. We find that, in many cases, modularity-based partitions do almost as well as our function-based method in finding functional communities, even though modularity does not specifically incorporate consideration of function.

Statistical mechanics of community detection

Physical Review E, 2006

Starting from a general ansatz, we show how community detection can be interpreted as finding the ground state of an infinite range spin glass. Our approach applies to weighted and directed networks alike. It contains the at hoc introduced quality function from [1] and the modularity Q as defined by Newman and Girvan [2] as special cases. The community structure of the network is interpreted as the spin configuration that minimizes the energy of the spin glass with the spin states being the community indices. We elucidate the properties of the ground state configuration to give a concise definition of communities as cohesive subgroups in networks that is adaptive to the specific class of network under study. Further we show, how hierarchies and overlap in the community structure can be detected. Computationally effective local update rules for optimization procedures to find the ground state are given. We show how the ansatz may be used to discover the community around a given node without detecting all communities in the full network and we give benchmarks for the performance of this extension. Finally, we give expectation values for the modularity of random graphs, which can be used in the assessment of statistical significance of community structure.

Robust detection of dynamic community structure in networks

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2013

We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations ("optimization variance") and over randomizations of network structure ("randomization variance"). Because the modularity quality function typically has a large number of nearly degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data.

Multi-scale modularity in complex networks

Modeling and Optimization in Mobile, Ad Hoc …, 2010

We focus on the detection of communities in multi-scale networks, namely networks made of different levels of organization and in which modules exist at different scales. It is first shown that methods based on modularity are not appropriate to uncover modules in empirical networks, mainly because modularity optimization has an intrinsic bias towards partitions having a characteristic number of modules which might not be compatible with the modular organization of the system. We argue for the use of more flexible quality functions ...

Community structure detection from networks with weighted modularity

Pattern Recognition Letters, 2019

Community detection from networks is an emerging topic in modern network science. Communities are defined as clusters of nodes or vertices that share higher concentration of edges among themselves than sharing with other nodes in the network. Community structure is an important property of real systems and detecting communities enables us to better understand the underlying structure of the system. The most widely used method for community detection is modularity maximization which works by optimizing a quality function named modularity of the network partition. However, traditional modularity-based approaches generally have a resolution limit that prevents them from detecting communities that are sufficiently smaller compared to the whole network. In this work, we target to overcome the resolution limit of the modularity function by incorporating a weight term in the modularity formulation. We propose a community detection approach based on a community quality metric, named as weighted modularity. We validate the performance of the proposed method in several benchmark networks and show that the proposed method is promising in different settings.

On community structure in complex networks: challenges and opportunities

Applied Network Science

Community structure is one of the most relevant features encountered in numerous real-world applications of networked systems. Despite the tremendous effort of a large interdisciplinary community of scientists working on this subject over the past few decades to characterize, model, and analyze communities, more investigations are needed in order to better understand the impact of community structure and its dynamics on networked systems. Here, we first focus on generative models of communities in complex networks and their role in developing strong foundation for community detection algorithms. We discuss modularity and the use of modularity maximization as the basis for community detection. Then, we follow with an overview of the Stochastic Block Model and its different variants as well as inference of community structures from such models. Next, we focus on time evolving networks, where existing nodes and links can disappear, and in parallel new nodes and links may be introduced....

Detection of Communities in Complex Graphs Based on the Normalized Covariance Between Vertices

2015

Communities detection in graphs has been the subject of many algorithms. Recent methods seek to optimize a function of modularity indicating a maximum of relationships within communities and a minimum of inter-communities relations. This paper will be presented as follows, first, we present the state of the art in matters of detection methods of communities then we propose a method for detecting communities. This method works into two steps, the first step consist to split the graph into subgraphs by using the normalized covariance measurement and the second part allows to merge the sub-graphs by maximizing the modularity of the resulting graph.