Showing papers on "Modularity (networks) published in 2008"

Fast unfolding of communities in large networks

Abstract: We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection method in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2.6 million customers and by analyzing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad-hoc modular networks. .

Fast unfolding of communities in large networks

Abstract: We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks.

Benchmark graphs for testing community detection algorithms

Abstract: Community structure is one of the most important features of real networks and reveals the internal organization of the nodes. Many algorithms have been proposed but the crucial issue of testing, i.e., the question of how good an algorithm is, with respect to others, is still open. Standard tests include the analysis of simple artificial graphs with a built-in community structure, that the algorithm has to recover. However, the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks. Here we introduce a class of benchmark graphs, that account for the heterogeneity in the distributions of node degrees and of community sizes. We use this benchmark to test two popular methods of community detection, modularity optimization, and Potts model clustering. The results show that the benchmark poses a much more severe test to algorithms than standard benchmarks, revealing limits that may not be apparent at a first analysis.

On Modularity Clustering

Abstract: Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomerative approach.

Community Structure in Directed Networks

Abstract: We consider the problem of finding communities or modules in directed networks. In the past, the most common approach to this problem has been to ignore edge direction and apply methods developed for community discovery in undirected networks, but this approach discards potentially useful information contained in the edge directions. Here we show how the widely used community finding technique of modularity maximization can be generalized in a principled fashion to incorporate information contained in edge directions. We describe an explicit algorithm based on spectral optimization of the modularity and show that it gives demonstrably better results than previous methods on a variety of test networks, both real and computer generated.

Morphological Integration and Developmental Modularity

Abstract: Biological systems, from molecular complexes to whole organisms and ecological interactions, tend to have a modular organization. Modules are sets of traits that are internally integrated by interactions among traits, but are relatively independent from other modules. The interactions within modules rely on different mechanisms, depending on the context of a study. For morphological traits, modularity occurs in developmental, genetic, functional, and evolutionary contexts. A range of methods for quantifying integration and modularity in morphological data is available, and a number of comparative and experimental designs can be used to compare the different contexts. How development produces covariation between traits can have substantial implications for understanding genetic variation and the potential for evolutionary change, but research in this area has only begun and many questions remain unanswered.

Analysis of the structure of complex networks at different resolution levels

Abstract: Modular structure is ubiquitous in real-world complex networks, and its detection is important because it gives insights in the structure-functionality relationship. The standard approach is based on the optimization of a quality function, modularity, which is a relative quality measure for a partition of a network into modules. Recently some authors have pointed out that the optimization of modularity has a fundamental drawback: the existence of a resolution limit beyond which no modular structure can be detected even though these modules might have own entity. The reason is that several topological descriptions of the network coexist at different scales, which is, in general, a fingerprint of complex systems. Here we propose a method that allows for multiple resolution screening of the modular structure. The method has been validated using synthetic networks, discovering the predefined structures at all scales. Its application to two real social networks allows to find the exact splits reported in the literature, as well as the substructure beyond the actual split.

Revealing Modular Architecture of Human Brain Structural Networks by Using Cortical Thickness from MRI

Abstract: Modularity, presumably shaped by evolutionary constraints, underlies the functionality of most complex networks ranged from social to biological networks. However, it remains largely unknown in human cortical networks. In a previous study, we demonstrated a network of correlations of cortical thickness among specific cortical areas and speculated that these correlations reflected an underlying structural connectivity among those brain regions. Here, we further investigated the intrinsic modular architecture of the human brain network derived from cortical thickness measurement. Modules were defined as groups of cortical regions that are connected morphologically to achieve the maximum network modularity. We show that the human cortical network is organized into 6 topological modules that closely overlap known functional domains such as auditory/language, strategic/executive, sensorimotor, visual, and mnemonic processing. The identified structure-based modular architecture may provide new insights into the functionality of cortical regions and connections between structural brain modules. This study provides the first report of modular architecture of the structural network in the human brain using cortical thickness measurements.

Bayesian Approach to Network Modularity

Abstract: We present an efficient, principled, and interpretable technique for inferring module assignments and for identifying the optimal number of modules in a given network. We show how several existing methods for finding modules can be described as variant, special, or limiting cases of our work, and how the method overcomes the resolution limit problem, accurately recovering the true number of modules. Our approach is based on Bayesian methods for model selection which have been used with success for almost a century, implemented using a variational technique developed only in the past decade. We apply the technique to synthetic and real networks and outline how the method naturally allows selection among competing models.

Quantitative function for community detection.

Abstract: We propose a quantitative function for community partition---i.e., modularity density or $D$ value. We demonstrate that this quantitative function is superior to the widely used modularity $Q$ and also prove its equivalence with the objective function of the kernel $k$ means. Both theoretical and numerical results show that optimizing the new criterion not only can resolve detailed modules that existing approaches cannot achieve, but also can correctly identify the number of communities.

Modularity in developing business services by platform approach

Abstract: Purpose – This study aims to explore the literature related to modularity in developing and manufacturing physical products in order to employ the idea of modularity into the business services context.Design/methodology/approach – In order to answer the defined research question, the authors construct an empirically grounded model for modular service platform. The research design follows an abductive logic beginning with the construction of a theoretical pre‐understanding and elaborating upon it empirically. Streams of literature that are applied are service marketing and operations and product development and modularity research including product architecture design. In the empirical part of the study, the authors elaborate on these issues through a qualitative single case study.Findings – The results show that the developed modular service platform including four modularity dimensions: service, process, organisational and customer interface dimensions can be used to create value in business services.Ori...

Identifying network communities with a high resolution.

Abstract: Community structure is an important property of complex networks. The 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 modularity function $(Q)$. However, the problem of modularity optimization is NP-hard and the existing approaches often suffer from a 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 or with a higher accuracy than the existing algorithms. We also discuss two possible reasons that can cause the resolution limit problem and provide a method to distinguish them. 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 undetected.

The evolution of modularity in bacterial metabolic networks

Abstract: Deciphering the modular organization of metabolic networks and understanding how modularity evolves have attracted tremendous interest in recent years. Here, we present a comprehensive large scale characterization of modularity across the bacterial tree of life, systematically quantifying the modularity of the metabolic networks of >300 bacterial species. Three main determinants of metabolic network modularity are identified. First, network size is an important topological determinant of network modularity. Second, several environmental factors influence network modularity, with endosymbionts and mammal-specific pathogens having lower modularity scores than bacterial species that occupy a wider range of niches. Moreover, even among the pathogens, those that alternate between two distinct niches, such as insect and mammal, tend to have relatively high metabolic network modularity. Third, horizontal gene transfer is an important force that contributes significantly to metabolic modularity. We additionally reconstruct the metabolic network of ancestral bacterial species and examine the evolution of modularity across the tree of life. This reveals a trend of modularity decrease from ancestors to descendants that is likely the outcome of niche specialization and the incorporation of peripheral metabolic reactions.

Does technological modularity substitute for control? A study of alliance performance in software outsourcing

Abstract: Although control is presumed to be necessary to curb opportunism, its implementation in alliances can be costly and challenging. Paradoxically, some contemporary firms have counterintuitively developed successful alliances without extensive formal control. A widespread but untested assertion that might help reconcile this contradiction is that technological modularity reduces the need for alliance control. The objective of this study is to develop and test this assertion. Using data from 120 software outsourcing alliances, we show that, process control, outcome control, and modularity independently enhance alliance performance. However modularity and control are imperfect substitutes: modularity lowers the influence of process control but not of outcome control on alliance performance. Our theoretical development and empirical testing of the interactions of alliance control with modularity has significant implications for strategy theory and practice, which are also discussed. Copyright © 2008 John Wiley & Sons, Ltd.

Efficient modularity optimization by multistep greedy algorithm and vertex mover refinement.

Abstract: Identifying strongly connected substructures in large networks provides insight into their coarse-grained organization. Several approaches based on the optimization of a quality function, e.g., the modularity, have been proposed. We present here a multistep extension of the greedy algorithm (MSG) that allows the merging of more than one pair of communities at each iteration step. The essential idea is to prevent the premature condensation into few large communities. Upon convergence of the MSG a simple refinement procedure called "vertex mover" (VM) is used for reassigning vertices to neighboring communities to improve the final modularity value. With an appropriate choice of the step width, the combined MSG-VM algorithm is able to find solutions of higher modularity than those reported previously. The multistep extension does not alter the scaling of computational cost of the greedy algorithm.

Modularity in Process Models: Review and Effects

Abstract: The use of subprocesses in large process models is an important step in modeling practice to handle complexity. While there are several advantages attributed to such a modular design, including ease of reuse, scalability, and enhanced understanding, the lack of precise guidelines turns out to be a major impediment for applying modularity in a systematic way. In this paper we approach this area of research from a critical perspective. Our first contribution is a review of existing approaches to process model modularity. This review shows that aside from some limited insights, a systematic and grounded approach to finding the optimal modularization of a process model is missing. Therefore, we turned to modular process models from practice to study their merits. In particular, we set up an experiment involving professional process modelers and tested the effect of modularization on understanding. Our second contribution, stemming from this experiment, is that modularity appears to pay off. We discuss some of the limitations of our research and implications for future design-oriented approaches.

Understanding biological functions through molecular networks

Abstract: The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.

Organization of excitable dynamics in hierarchical biological networks.

Abstract: This study investigates the contributions of network topology features to the dynamic behavior of hierarchically organized excitable networks. Representatives of different types of hierarchical networks as well as two biological neural networks are explored with a three-state model of node activation for systematically varying levels of random background network stimulation. The results demonstrate that two principal topological aspects of hierarchical networks, node centrality and network modularity, correlate with the network activity patterns at different levels of spontaneous network activation. The approach also shows that the dynamic behavior of the cerebral cortical systems network in the cat is dominated by the network's modular organization, while the activation behavior of the cellular neuronal network of Caenorhabditis elegans is strongly influenced by hub nodes. These findings indicate the interaction of multiple topological features and dynamic states in the function of complex biological networks.

Does interfirm modularity complement ignorance? A field study of software outsourcing alliances

Abstract: Knowledge-intensive outsourcing alliances present outsourcers with a tension between simultaneously sharing enough private knowledge to accomplish alliance goals and safeguarding such knowledge against misappropriation. This study explores the perspective that increasing interfirm modularity lowers the need for interfirm knowledge sharing. Put another way, modularity complements outsourcee ignorance. Analyses of data on 209 alliances between U.S. firms and software services firms in Russia, Ireland, and India provide strong support for this idea. Our theoretical elaboration and empirical testing of the complementarities between modularity and outsourcee ignorance has significant implications for strategy theory, which are also discussed. Copyright © 2008 John Wiley & Sons, Ltd.

Fuzzy logic for cross-layer optimization in cognitive radio networks

Abstract: The search for the ultimate architecture for cross-layer optimization in cognitive radio networks is characterized by challenges such as modularity, interpretability, imprecision, scalability, and complexity constraints. In this article we propose fuzzy logic as an effective means of meeting these challenges, as far as both knowledge representation and control implementation are concerned.

Networks of innovation and modularity: a dynamic perspective

Abstract: The aim of this paper is to provide a comprehensive perspective for understanding the dynamics of modularity and the implications of those dynamics for innovation networks. The main contention of this paper is that the dynamics of technology development should reflect the dynamics of a firm network. During the early development of a technology, when the interactions among component types are unclear (in a state of flux) and, therefore, difficult to codify and freeze, organisations build connections with research centres and universities to explore alternative technological solutions. Once such interactions are better understood, codified, modularised and shared, then more exploitative networks (e.g., with suppliers and customers) may be better suited to exploit the current technology. In the transition from the early development phase to the more mature phase, firms must build ties to startups and new entrants, because these firms experiment with alternative design configurations that exploit the underlying technology. In addition, during this transition stage, firms must connect to third-party firms, since the supporting investments made by these firms may determine which of the alternative configurations will become 'the standard'. During this stage, the relationships across firms are defined and governed by modular interfaces that are, in turn, dictated by product interfaces.

Motif-based communities in complex networks

Abstract: Community definitions usually focus on edges, inside and between the communities. However, the high density of edges within a community determines correlations between nodes going beyond nearest neighbors, and which are indicated by the presence of motifs. We show how motifs can be used to define general classes of nodes, including communities, by extending the mathematical expression of Newman?Girvan modularity. We construct then a general framework and apply it to some synthetic and real networks.

Spontaneous emergence of modularity in cellular networks.

Abstract: Modularity is known to be one of the most relevant characteristics of biological systems and appears to be present at multiple scales. Given its adaptive potential, it is often assumed to be the target of selective pressures. Under such interpretation, selection would be actively favouring the formation of modular structures, which would specialize in different functions. Here we show that, within the context of cellular networks, no such selection pressure is needed to obtain modularity. Instead, the intrinsic dynamics of network growth by duplication and diversification is able to generate it for free and explain the statistical features exhibited by small subgraphs. The implications for the evolution and evolvability of both biological and technological systems are discussed.

Semantic Modularity and Module Extraction in Description Logics

Abstract: The aim of this paper is to study semantic notions of modularity in description logic (DL) terminologies and reasoning problems that are relevant for modularity. We define two notions of a module whose independence is formalised in a model-theoretic way. Focusing mainly on the DLs EL and ALC, we then develop algorithms for module extraction, for checking whether a part of a terminology is a module, and for a number of related problems. We also analyse the complexity of these problems, which ranges from tractable to undecidable. Finally, we provide an experimental evaluation of our module extraction algorithms based on the large-scale terminology SNOMED CT.

Centrality, Network Capacity, and Modularity as Parameters to Analyze the Core-Periphery Structure in Metabolic Networks

Abstract: Genome-scale metabolic networks of organisms are normally very large and complex. Previous studies have shown that they are organized in a hierarchical and modular manner. In particular, a core-periphery modular organization structure has been proposed for metabolic networks. However, no methods or parameters are available in the literature to quantitatively evaluate or find the hierarchical and modular structure of metabolic networks. In this paper, we propose a parameter called ldquocore coefficientrdquo to quantitatively evaluate the core-periphery structure of a metabolic network. This parameter is defined based on the concept of closeness centrality of metabolites and a newly defined parameter: network capacity. To find or define the core and the periphery modules of a metabolic network, we further developed a method to decompose metabolic networks based on a quantitative parameter of modularity and a procedure of core extraction. The method has been developed with genome-scale metabolic networks of five representative organisms, which include Aeropyrum pernix, Bacillus subtilis, Escherichia coli, Saccharomyces cerevisiae, and Homo sapiens . The results were compared with two artificially generated network models.

Age-dependent evolution of the yeast protein interaction network suggests a limited role of gene duplication and divergence.

Abstract: Proteins interact in complex protein–protein interaction (PPI) networks whose topological properties—such as scale-free topology, hierarchical modularity, and dissortativity—have suggested models of network evolution. Currently preferred models invoke preferential attachment or gene duplication and divergence to produce networks whose topology matches that observed for real PPIs, thus supporting these as likely models for network evolution. Here, we show that the interaction density and homodimeric frequency are highly protein age–dependent in real PPI networks in a manner which does not agree with these canonical models. In light of these results, we propose an alternative stochastic model, which adds each protein sequentially to a growing network in a manner analogous to protein crystal growth (CG) in solution. The key ideas are (1) interaction probability increases with availability of unoccupied interaction surface, thus following an anti-preferential attachment rule, (2) as a network grows, highly connected sub-networks emerge into protein modules or complexes, and (3) once a new protein is committed to a module, further connections tend to be localized within that module. The CG model produces PPI networks consistent in both topology and age distributions with real PPI networks and is well supported by the spatial arrangement of protein complexes of known 3-D structure, suggesting a plausible physical mechanism for network evolution.

A Statistical Framework for Testing Modularity in Multidimensional Data

Abstract: Modular variation of multivariate traits results from modular distribution of effects of genetic and epigenetic interactions among those traits However, statistical methods rarely detect truly modular patterns, possibly because the processes that generate intramodular associations may overlap spatially Methodologically, this overlap may cause multiple patterns of modularity to be equally consistent with observed covariances To deal with this indeterminacy, the present study outlines a framework for testing a priori hypotheses of modularity in which putative modules are mathematically represented as multidimensional subspaces embedded in the data Model expectations are computed by subdividing the data into arrays of variables, and intermodular interactions are represented by overlapping arrays Covariance structures are thus modeled as the outcome of complex and nonorthogonal intermodular interactions This approach is demonstrated by analyzing mandibular modularity in nine rodent species A total of 620 models are fit to each species, and the most strongly supported are heuristically modified to improve their fit Five modules common to all species are identified, which approximately map to the developmental modules of the mandible Within species, these modules are embedded within larger “super-modules,” suggesting that these conserved modules act as building blocks from which covariation patterns are built

Automatic Modular Assembly System and its Distributed Control

Abstract: Construction is difficult to automate because of its complexity. Introducing modularity into both structural components and a means of assembly solves the problem by simplifying the construction task. Based on this idea, we propose a novel concept of a fully automated construction system called the Automatic Modular Assembly System (AMAS). In this paper, we discuss the hardware system and distributed control method of AMAS. This system uses passive building blocks called “structure modules” and an assembler robot that is specialized to handle them. This “modular” concept drastically simplifies structural complexity. We have built a prototype model to evaluate its automatic construction capability. Then we introduce a distributed autonomous control for AMAS, which uses a gradient field to indicate the directions to the assembler robots. The gradient field is generated on the structure modules. To improve the efficiency, we introduce collision avoidance rules such as module relay and local negotiation via a blackboard. We also evaluate the overall performance of the distributed control with simulations.

Multistep greedy algorithm identifies community structure in real-world and computer-generated networks

Abstract: We have recently introduced a multistep extension of the greedy algorithm for modularity optimization. The extension is based on the idea that merging l pairs of communities (l>1) at each iteration prevents premature condensation into few large communities. Here, an empirical formula is presented for the choice of the step width l that generates partitions with (close to) optimal modularity for 17 real-world and 1100 computer-generated networks. Furthermore, an in-depth analysis of the communities of two real-world networks (the metabolic network of the bacterium E. coli and the graph of coappearing words in the titles of papers coauthored by Martin Karplus) provides evidence that the partition obtained by the multistep greedy algorithm is superior to the one generated by the original greedy algorithm not only with respect to modularity, but also according to objective criteria. In other words, the multistep extension of the greedy algorithm reduces the danger of getting trapped in local optima of modularity and generates more reasonable partitions.

Modularity of stress response evolution

Abstract: Responses to extracellular stress directly confer survival fitness by means of complex regulatory networks. Despite their complexity, the networks must be evolvable because of changing ecological and environmental pressures. Although the regulatory networks underlying stress responses are characterized extensively, their mechanism of evolution remains poorly understood. Here, we examine the evolution of three candidate stress response networks (chemotaxis, competence for DNA uptake, and endospore formation) by analyzing their phylogenetic distribution across several hundred diverse bacterial and archaeal lineages. We report that genes in the chemotaxis and sporulation networks group into well defined evolutionary modules with distinct functions, phenotypes, and substitution rates as compared with control sets of randomly chosen genes. The evolutionary modules vary in both number and cohesiveness among the three pathways. Chemotaxis has five coherent modules whose distribution among species shows a clear pattern of interdependence and rewiring. Sporulation, by contrast, is nearly monolithic and seems to be inherited vertically, with three weak modules constituting early and late stages of the pathway. Competence does not seem to exhibit well defined modules either at or below the pathway level. Many of the detected modules are better understood in engineering terms than in protein functional terms, as we demonstrate using a control-based ontology that classifies gene function according to roles such as “sensor,” “regulator,” and “actuator.” Moreover, we show that combinations of the modules predict phenotype, yet surprisingly do not necessarily correlate with phylogenetic inheritance. The architectures of these three pathways are therefore emblematic of different modes and constraints on evolution.