Showing papers on "Modularity (networks) published in 2012"

The entorhinal grid map is discretized

Abstract: The medial entorhinal cortex (MEC) is part of the brain's circuit for dynamic representation of self-location. The metric of this representation is provided by grid cells, cells with spatial firing fields that tile environments in a periodic hexagonal pattern. Limited anatomical sampling has obscured whether the grid system operates as a unified system or a conglomerate of independent modules. Here we show with recordings from up to 186 grid cells in individual rats that grid cells cluster into a small number of layer-spanning anatomically overlapping modules with distinct scale, orientation, asymmetry and theta-frequency modulation. These modules can respond independently to changes in the geometry of the environment. The discrete topography of the grid-map, and the apparent autonomy of the modules, differ from the graded topography of maps for continuous variables in several sensory systems, raising the possibility that the modularity of the grid map is a product of local self-organizing network dynamics.

A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks

Abstract: The human brain is organized in functional modules. Such an organization presents a basic conundrum: Modules ought to be sufficiently independent to guarantee functional specialization and sufficiently connected to bind multiple processors for efficient information transfer. It is commonly accepted that small-world architecture of short paths and large local clustering may solve this problem. However, there is intrinsic tension between shortcuts generating small worlds and the persistence of modularity, a global property unrelated to local clustering. Here, we present a possible solution to this puzzle. We first show that a modified percolation theory can define a set of hierarchically organized modules made of strong links in functional brain networks. These modules are “large-world” self-similar structures and, therefore, are far from being small-world. However, incorporating weaker ties to the network converts it into a small world preserving an underlying backbone of well-defined modules. Remarkably, weak ties are precisely organized as predicted by theory maximizing information transfer with minimal wiring cost. This trade-off architecture is reminiscent of the “strength of weak ties” crucial concept of social networks. Such a design suggests a natural solution to the paradox of efficient information flow in the highly modular structure of the brain.

Robust Detection of Dynamic Community Structure in Networks

Abstract: 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.

Simple models of human brain functional networks

Abstract: Human brain functional networks are embedded in anatomical space and have topological properties—small-worldness, modularity, fat-tailed degree distributions—that are comparable to many other complex networks. Although a sophisticated set of measures is available to describe the topology of brain networks, the selection pressures that drive their formation remain largely unknown. Here we consider generative models for the probability of a functional connection (an edge) between two cortical regions (nodes) separated by some Euclidean distance in anatomical space. In particular, we propose a model in which the embedded topology of brain networks emerges from two competing factors: a distance penalty based on the cost of maintaining long-range connections; and a topological term that favors links between regions sharing similar input. We show that, together, these two biologically plausible factors are sufficient to capture an impressive range of topological properties of functional brain networks. Model parameters estimated in one set of functional MRI (fMRI) data on normal volunteers provided a good fit to networks estimated in a second independent sample of fMRI data. Furthermore, slightly detuned model parameters also generated a reasonable simulation of the abnormal properties of brain functional networks in people with schizophrenia. We therefore anticipate that many aspects of brain network organization, in health and disease, may be parsimoniously explained by an economical clustering rule for the probability of functional connectivity between different brain areas.

Graph spectra and the detectability of community structure in networks

Abstract: We study networks that display community structure--groups of nodes within which connections are unusually dense. Using methods from random matrix theory, we calculate the spectra of such networks in the limit of large size, and hence demonstrate the presence of a phase transition in matrix methods for community detection, such as the popular modularity maximization method. The transition separates a regime in which such methods successfully detect the community structure from one in which the structure is present but is not detected. By comparing these results with recent analyses of maximum-likelihood methods, we are able to show that spectral modularity maximization is an optimal detection method in the sense that no other method will succeed in the regime where the modularity method fails.

Functional brain network modularity captures inter- and intra-individual variation in working memory capacity

Abstract: Background Cognitive abilities, such as working memory, differ among people; however, individuals also vary in their own day-to-day cognitive performance. One potential source of cognitive variability may be fluctuations in the functional organization of neural systems. The degree to which the organization of these functional networks is optimized may relate to the effective cognitive functioning of the individual. Here we specifically examine how changes in the organization of large-scale networks measured via resting state functional connectivity MRI and graph theory track changes in working memory capacity. Methodology/Principal Findings Twenty-two participants performed a test of working memory capacity and then underwent resting-state fMRI. Seventeen subjects repeated the protocol three weeks later. We applied graph theoretic techniques to measure network organization on 34 brain regions of interest (ROI). Network modularity, which measures the level of integration and segregation across sub-networks, and small-worldness, which measures global network connection efficiency, both predicted individual differences in memory capacity; however, only modularity predicted intra-individual variation across the two sessions. Partial correlations controlling for the component of working memory that was stable across sessions revealed that modularity was almost entirely associated with the variability of working memory at each session. Analyses of specific sub-networks and individual circuits were unable to consistently account for working memory capacity variability. Conclusions/Significance The results suggest that the intrinsic functional organization of an a priori defined cognitive control network measured at rest provides substantial information about actual cognitive performance. The association of network modularity to the variability in an individual's working memory capacity suggests that the organization of this network into high connectivity within modules and sparse connections between modules may reflect effective signaling across brain regions, perhaps through the modulation of signal or the suppression of the propagation of noise.

Community structure and the spread of infectious disease in primate social networks

Abstract: Living in a large social group is thought to increase disease risk in wild animal populations, but comparative studies have provided mixed support for this prediction. Here, we take a social network perspective to investigate whether patterns of social contact within groups influence parasite risk. Specifically, increased modularity (i.e. sub-grouping) in larger groups could offset the increased disease risk associated with living in a large group. We simulated the spread of a contagious pathogen in random social networks to generate theoretically grounded predictions concerning the relationship between social network connectivity and the success of socially transmitted pathogens. Simulations yielded the prediction that community modularity (Q) negatively impacts parasite success. No clear predictions emerged for a second network metric we considered, the eigenvector centralization index (C), as the relationship between this measure and parasite success depended on the transmission probability of parasites. We then tested the prediction that Q reduces parasite success in a phylogenetic comparative analysis of social network modularity and parasite richness across 19 primate species. Using a Bayesian implementation of phylogenetic generalized least squares and controlling for sampling effort, we found that primates living in larger groups exhibited higher Q, and as predicted by our simulations, higher Q was associated with lower richness of socially transmitted parasites. This suggests that increased modularity mediates the elevated risk of parasitism associated with living in larger groups, which could contribute to the inconsistent findings of empirical studies on the association between group size and parasite risk. Our results indicate that social networks may play a role in mediating pressure from socially transmitted parasites, particularly in large groups where opportunities for transmitting communicable diseases are abundant. We propose that parasite pressure in gregarious primates may have favored the evolution of behaviors that increase social network modularity, especially in large social groups.

Beyond the “Mirroring” Hypothesis: Product Modularity and Interorganizational Relations in the Air Conditioning Industry

Abstract: This study explores whether, to what extent, and under which conditions modular products are associated with modular organizations (the “mirroring” hypothesis). We analyze the product and organizational architectures of three firms in the air conditioning industry through an original data set of 100 components and supply relationships. Applying a variety of regression methods, we show that, under the condition of product architecture stability at the component level, supplier relations for loosely coupled components are characterized by less information sharing, which implies that the degree of coupling of product components varies directly with the degree of coupling of organizations (the “mirroring” hypothesis). Also, the performance of supply relationships depends on the amount of buyer–supplier information sharing but not on the degree of component modularity, which supports the relational view and confirms that product modularity does not have unambiguous effects on organizational performance. Moreover, the degree of component modularity negatively moderates the impact of buyer–supplier information sharing on supplier-relationship performance, which confirms that component modularity works as an ex ante, embedded substitute for high-powered interorganizational integration mechanisms. Finally, contingent on firms' strategies, organizational structures, and capabilities, we argue that at the firm level, higher product modularity may be associated either with less information sharing with suppliers, which implies that the mirroring effect might hold also at the firm level, or with more information sharing with suppliers, which implies that there may be increasing returns to modularity in design efforts because of interorganizational integration (the “complementarity” hypothesis).

Phylogenetic signal in module composition and species connectivity in compartmentalized host-parasite networks.

Abstract: Across different taxa, networks of mutualistic or antag- onistic interactions show consistent architecture. Most networks are modular, with modules being distinct species subsets connected mainly with each other and having few connections to other modules. We investigate the phylogenetic relatedness of species within modules and whether a phylogenetic signal is detectable in the within- and among-module connectivity of species using 27 mammal-flea net- works from the Palaearctic. In the 24 networks that were modular, closely related hosts co-occurred in the same module more often than expected by chance; in contrast, this was rarely the case for parasites. The within- and among-module connectivity of the same host or parasite species varied geographically. However, among-mod- ule but not within-module connectivity of host and parasites was somewhat phylogenetically constrained. These findings suggest that the establishment of host-parasite networks results from the interplay between phylogenetic influences acting mostly on hosts and local factors acting on parasites, to create an asymmetrically constrained pattern of geographic variation in modular structure. Modularity in host-parasite networks seems to result from the shared evolutionary history of hosts and by trait convergence among unrelated parasites. This suggests profound differences between hosts and parasites in the establishment and functioning of bipartite antagonistic networks.

Roles for modularity and constraint in the evolution of cranial diversity among Anolis lizards.

Abstract: Complex organismal structures are organized into modules, suites of traits that develop, function, and vary in a coordinated fashion By limiting or directing covariation among component traits, modules are expected to represent evolutionary building blocks and to play an important role in morphological diversification But how stable are patterns of modularity over macroevolutionary timescales? Comparative analyses are needed to address the macroevolutionary effect of modularity, but to date few have been conducted We describe patterns of skull diversity and modularity in Caribbean Anolis lizards We first diagnose the primary axes of variation in skull shape and then examine whether diversification of skull shape is concentrated to changes within modules or whether changes arose across the structure as a whole We find no support for the hypothesis that cranial modules are conserved as species diversify in overall skull shape Instead we find that anole skull shape and modularity patterns independently converge In anoles, skull modularity is evolutionarily labile and may reflect the functional demands of unique skull shapes Our results suggest that constraints have played little role in limiting or directing the diversification of head shape in Anolis lizards

The Emergence of Modularity in Biological Systems

Abstract: In this review, we discuss modularity and hierarchy in biological systems. We review examples from protein structure, genetics, and biological networks of modular partitioning of the geometry of biological space. We review theories to explain modular organization of biology, with a focus on explaining how biology may spontaneously organize to a structured form. That is, we seek to explain how biology nucleated from among the many possibilities in chemistry. The emergence of modular organization of biological structure will be described as a symmetry-breaking phase transition, with modularity as the order parameter. Experimental support for this description will be reviewed. Examples will be presented from pathogen structure, metabolic networks, gene networks, and protein-protein interaction networks. Additional examples will be presented from ecological food networks, developmental pathways, physiology, and social networks.

Are automatically-detected code anomalies relevant to architectural modularity?: an exploratory analysis of evolving systems

Abstract: As software systems are maintained, their architecture modularity often degrades through architectural erosion and drift. More directly, however, the modularity of software implementations degrades through the introduction of code anomalies, informally known as code smells. A number of strategies have been developed for supporting the automatic identification of implementation anomalies when only the source code is available. However, it is still unknown how reliable these strategies are when revealing code anomalies related to erosion and drift processes. In this paper, we present an exploratory analysis that investigates to what extent the automatically-detected code anomalies are related to problems that occur with an evolving system's architecture. We analyzed code anomaly occurrences in 38 versions of 5 applications using existing detection strategies. The outcome of our evaluation suggests that many of the code anomalies detected by the employed strategies were not related to architectural problems. Even worse, over 50% of the anomalies not observed by the employed techniques (false negatives) were found to be correlated with architectural problems.

Self-similar scaling of density in complex real-world networks

Abstract: Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome of the evolution of real-world systems has also attracted much attention within the physics literature. Here we investigate the scaling of density in complex networks under two classical box-covering renormalizations–network coarse-graining–and also different community-based renormalizations. The analysis on over 50 real-world networks reveals a power-law scaling of network density and size under adequate renormalization technique, yet irrespective of network type and origin. The results thus advance a recent discovery of a universal scaling of density among different real-world networks [P.J. Laurienti, K.E. Joyce, Q.K. Telesford, J.H. Burdette, S. Hayasaka, Universal fractal scaling of self-organized networks, Physica A 390 (20) (2011) 3608–3613] and imply an existence of a scale-free density also within–among different self-similar scales of–complex real-world networks. The latter further improves the comprehension of self-similar structure in large real-world networks with several possible applications.

The conundrum of functional brain networks: small-world efficiency or fractal modularity.

Abstract: The human brain has been studied at multiple scales, from neurons, circuits, areas with well-defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that were inter-connected in a small-world topology. Here, we provide more details on the use of network science tools to elaborate on this behavior. We indicate the importance of using percolation theory to highlight the modular character of the functional brain network. These modules present a fractal, self-similar topology, identified through fractal network methods. When we lower the threshold of correlations to include weaker ties, the network as a whole assumes a small-world character. These weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs.

Communities and Balance in Signed Networks: A Spectral Approach

Abstract: Discussion based websites like Epinions.com and Slashdot.com allow users to identify both friends and foes. Such networks are called Signed Social Networks and mining communities of like-minded users from these networks has potential value. We extend existing community detection algorithms that work only on unsigned networks to be applicable to signed networks. In particular, we develop a spectral approach augmented with iterative optimization. We use our algorithms to study both communities and structural balance. Our results indicate that modularity based communities are distinct from structurally balanced communities.

Using ecological network theory to evaluate the causes and consequences of arbuscular mycorrhizal community structure.

Abstract: Arbuscular mycorrhizal fungi (AMF) are widespread and their symbiotic interactions involve the majority of terrestrial plant species (Wang & Qiu, 2006). These obligate biotrophs generally improve the nutrition and vigor of the host, thereby affecting individual plant traits (van der Heijden et al., 1998) as well as the composition and functioning of entire plant communities (Moora & Zobel, 1996; Hartnett & Wilson, 1999; Bever, 2002). Studies on individual plant traits are useful in determining fitness benefits to the plant (e.g. increased growth, resistance to pathogens, etc.), whereas studies on community-level interactions can potentially explain constraints on host–symbiont web architecture (e.g. Bluthgen et al., 2007). Community-level studies have been limited, however, to small subsets of natural plant communities, because processing and identifying AMF species associated with numerous plant root systems have proven costly and painstaking. Recent advances in next-generation sequencing technologies (Margulies et al., 2005) have removed this hurdle and improved the detection of rare AMF species (Opik et al., 2009). This increased capacity in describing whole plant–AMF networks provides an opportunity to identify the causes, and assess the functional consequences, of symbiotic network architectures (i.e. topology). Network theory, originally developed to describe the flow of information within computational and social networks (Emerson, 1972), has more recently been applied to ecological studies of various mutualistic systems (Jordano et al., 2003; Olesen et al., 2007; Joppa et al., 2010). The major advantage of an ecological network approach is that topological metrics can be quantified for any given network involving two or more groups of interacting organisms (e.g. plants and pollinators, food webs, etc.). For example, ecological networks may be described in terms of their ‘nestedness’. High nestedness occurs when specialist species interact with a subset of partners with which generalist species also interact. For example, a specialist pollinator would tend to specialize on a generalist plant, and vice versa (Fig. 1a). This absence of reciprocal specialization was shown to be a pervasive feature of pollination networks (Bascompte et al., 2003; Joppa et al., 2009, 2010) that potentially favors diversity and stability of ecological communities (Memmott et al., 2004; Burgos et al., 2007; Bastolla et al., 2009; Thébault & Fontaine, 2010). Ecological networks can also be described according to their ‘modularity’, that is, the tendency of species to be grouped into modules in which interactions are more frequent than with the rest of the community (Fig. 1b). Thompson (2005) suggested that communities may assemble into distinct modules based on the functional complementarity of their traits, and this may offer some insight into coevolutionary dynamics between symbiotic species (Guimarães et al., 2007). In this Letter, we argue that an ecological network approach could provide a framework by which to characterize and compare plant–AMF communities from different environments or at different successional stages. This, in turn, could improve our understanding of mechanisms structuring mycorrhizal communities and bring mycorrhizal science to a more predictive level (Johnson et al., 2006). In a recent study, Opik et al. (2009) used pyrosequencing to describe AMF communities associated with 10 plant species in a forest understory community. Here, we have used their published data set to demonstrate the applicability of ecological network theory to characterize plant–AMF communities. Our exercise revealed that this particular plant–AMF network was both highly nested and modular. We discuss possible reasons and implications for such topological features, Forum

The community structure of SAT formulas

Abstract: The research community on complex networks has developed techniques of analysis and algorithms that can be used by the SAT community to improve our knowledge about the structure of industrial SAT instances. It is often argued that modern SAT solvers are able to exploit this hidden structure, without a precise definition of this notion. In this paper, we show that most industrial SAT instances have a high modularity that is not present in random instances. We also show that successful techniques, like learning, (indirectly) take into account this community structure. Our experimental study reveal that most learnt clauses are local on one of those modules or communities.

Quantitative Function for Community Detection

Abstract: Detecting and characterizing the community structure of complex network is fundamental. We compare the classical optimization indexes of modularity and modularity density, which are quality indexes for a partition of a network into communities. Based on this, we propose a quantitative function for community partition, named communitarity or C value. We demonstrate that the quantitative is superior to modularity Q and modularity density D. Both theoretical and numerical results show that optimizing the new index not only can resolve small modules, but also can correctly identify the number of communities.

Constraint and Opportunity: The Genetic Basis and Evolution of Modularity in the Cichlid Mandible

Abstract: Modular variation, whereby the relative degree of connectivity varies within a system, is thought to evolve through a process of selection that favors the integration of certain traits and the decoupling of others. In this way, modularity may facilitate the pace of evolution and determine evolvability. Alternatively, conserved patterns of modularity may act to constrain the rate and direction of evolution by preventing certain functions from evolving. A comprehensive understanding of the potential interplay between these phenomena will require knowledge of the inheritance and the genetic basis of modularity. Here we explore these ideas in the cichlid mandible by investigating patterns of modularity at the clade and species levels and through the introduction of a new approach, the individual level. Specifically, we assessed patterns of covariation in Lake Malawi cichlid species that employ alternate “biting” and “suction-feeding” modes of feeding and in a hybrid cross between these two ecotypes. A...

Communities and bottlenecks: trees and treelike networks have high modularity.

Abstract: Much effort has gone into understanding the modular nature of complex networks. Communities, also known as clusters or modules, are typically considered to be densely interconnected groups of nodes that are only sparsely connected to other groups in the network. Discovering high quality communities is a difficult and important problem in a number of areas. The most popular approach is the objective function known as modularity, used both to discover communities and to measure their strength. To understand the modular structure of networks it is then crucial to know how such functions evaluate different topologies, what features they account for, and what implicit assumptions they may make. We show that trees and treelike networks can have unexpectedly and often arbitrarily high values of modularity. This is surprising since trees are maximally sparse connected graphs and are not typically considered to possess modular structure, yet the nonlocal null model used by modularity assigns low probabilities, and thus high significance, to the densities of these sparse tree communities. We further study the practical performance of popular methods on model trees and on a genealogical data set and find that the discovered communities also have very high modularity, often approaching its maximum value. Statistical tests reveal the communities in trees to be significant, in contrast with known results for partitions of sparse, random graphs.

Creating and analyzing pathway and protein interaction compendia for modelling signal transduction networks.

Abstract: Background: Understanding the information-processing capabilities of signal transduction networks, how those networks are disrupted in disease, and rationally designing therapies to manipulate diseased states require systematic and accurate reconstruction of network topology. Data on networks central to human physiology, such as the inflammatory signalling networks analyzed here, are found in a multiplicity of on-line resources of pathway and interactome databases (Cancer CellMap, GeneGo, KEGG, NCI-Pathway Interactome Database (NCI-PID), PANTHER, Reactome, I2D, and STRING). We sought to determine whether these databases contain overlapping information and whether they can be used to construct high reliability prior knowledge networks for subsequent modeling of experimental data. Results: We have assembled an ensemble network from multiple on-line sources representing a significant portion of all machine-readable and reconcilable human knowledge on proteins and protein interactions involved in inflammation. This ensemble network has many features expected of complex signalling networks assembled from high-throughput data: a power law distribution of both node degree and edge annotations, and topological features of a “bow tie” architecture in which diverse pathways converge on a highly conserved set of enzymatic cascades focused around PI3K/ AKT, MAPK/ERK, JAK/STAT, NFκB, and apoptotic signaling. Individual pathways exhibit “fuzzy” modularity that is statistically significant but still involving a majority of “cross-talk” interactions. However, we find that the most widely used pathway databases are highly inconsistent with respect to the actual constituents and interactions in this network. Using a set of growth factor signalling networks as examples (epidermal growth factor, transforming growth factor-beta, tumor necrosis factor, and wingless), we find a multiplicity of network topologies in which receptors couple to downstream components through myriad alternate paths. Many of these paths are inconsistent with well-established mechanistic features of signalling networks, such as a requirement for a transmembrane receptor in sensing extracellular ligands. Conclusions: Wide inconsistencies among interaction databases, pathway annotations, and the numbers and identities of nodes associated with a given pathway pose a major challenge for deriving causal and mechanistic insight from network graphs. We speculate that these inconsistencies are at least partially attributable to cell, and context-specificity of cellular signal transduction, which is largely unaccounted for in available databases, but the absence of standardized vocabularies is an additional confounding factor. As a result of discrepant annotations, it is very difficult to identify biologically meaningful pathways from interactome networks ap riori. However, by incorporating prior knowledge, it is possible to successively build out network complexity with high confidence from a simple linear signal transduction scaffold. Such reduced complexity networks appear suitable for use in mechanistic models while being richer and better justified than the simple linear pathways usually depicted in diagrams of signal transduction.

Community Detection in Dynamic Social Networks Based on Multiobjective Immune Algorithm

Abstract: Community structure is one of the most important properties in social networks, and community detection has received an enormous amount of attention in recent years. In dynamic networks, the communities may evolve over time so that pose more challenging tasks than in static ones. Community detection in dynamic networks is a problem which can naturally be formulated with two contradictory objectives and consequently be solved by multiobjective optimization algorithms. In this paper, a novel multiobjective immune algorithm is proposed to solve the community detection problem in dynamic networks. It employs the framework of nondominated neighbor immune algorithm to simultaneously optimize the modularity and normalized mutual information, which quantitatively measure the quality of the community partitions and temporal cost, respectively. The problem-specific knowledge is incorporated in genetic operators and local search to improve the effectiveness and efficiency of our method. Experimental studies based on four synthetic datasets and two real-world social networks demonstrate that our algorithm can not only find community structure and capture community evolution more accurately but also be more steadily than the state-of-the-art algorithms.

Creating and analyzing pathway and protein interaction compendia for modelling signal transduction networks

Abstract: Background: Understanding the information-processing capabilities of signal transduction networks, how those networks are disrupted in disease, and rationally designing therapies to manipulate diseased states require systematic and accurate reconstruction of network topology. Data on networks central to human physiology, such as the inflammatory signalling networks analyzed here, are found in a multiplicity of on-line resources of pathway and interactome databases (Cancer CellMap, GeneGo, KEGG, NCI-Pathway Interactome Database (NCI-PID), PANTHER, Reactome, I2D, and STRING). We sought to determine whether these databases contain overlapping information and whether they can be used to construct high reliability prior knowledge networks for subsequent modeling of experimental data. Results: We have assembled an ensemble network from multiple on-line sources representing a significant portion of all machine-readable and reconcilable human knowledge on proteins and protein interactions involved in inflammation. This ensemble network has many features expected of complex signalling networks assembled from high-throughput data: a power law distribution of both node degree and edge annotations, and topological features of a “bow tie” architecture in which diverse pathways converge on a highly conserved set of enzymatic cascades focused around PI3K/ AKT, MAPK/ERK, JAK/STAT, NFκB, and apoptotic signaling. Individual pathways exhibit “fuzzy” modularity that is statistically significant but still involving a majority of “cross-talk” interactions. However, we find that the most widely used pathway databases are highly inconsistent with respect to the actual constituents and interactions in this network. Using a set of growth factor signalling networks as examples (epidermal growth factor, transforming growth factor-beta, tumor necrosis factor, and wingless), we find a multiplicity of network topologies in which receptors couple to downstream components through myriad alternate paths. Many of these paths are inconsistent with well-established mechanistic features of signalling networks, such as a requirement for a transmembrane receptor in sensing extracellular ligands. Conclusions: Wide inconsistencies among interaction databases, pathway annotations, and the numbers and identities of nodes associated with a given pathway pose a major challenge for deriving causal and mechanistic insight from network graphs. We speculate that these inconsistencies are at least partially attributable to cell, and context-specificity of cellular signal transduction, which is largely unaccounted for in available databases, but the absence of standardized vocabularies is an additional confounding factor. As a result of discrepant annotations, it is very difficult to identify biologically meaningful pathways from interactome networks ap riori. However, by incorporating prior knowledge, it is possible to successively build out network complexity with high confidence from a simple linear signal transduction scaffold. Such reduced complexity networks appear suitable for use in mechanistic models while being richer and better justified than the simple linear pathways usually depicted in diagrams of signal transduction.

Comparative analysis of coupling modularity metrics

Abstract: Modular design has become a widely accepted developmental strategy to create products and systems that can be easily manufactured, upgraded and maintained. In order to achieve these benefits through improvement of a system's modularity, it must be measured. An ideal measure ought to capture modularity while being independent of other architectural factors such as size, system coupling density or the number of modules. In this work, we review past research on modularity measures. Eight modularity measures are selected for a detailed analysis. We use a design of experiments approach to analyse which metrics best measure the degree of modularity independent of other irrelevant factors. To do this, we conduct a factorial analysis of 24 canonical architectures with idealised modularity, including precisely integral, modular and bus architectures. We find that most measures produce inconsistent results, especially if the system architecture contains a bus or modules with loose internal coupling. We identify the...

A spin-glass model for semi-supervised community detection

Abstract: Current modularity-based community detection methods show decreased performance as relational networks become increasingly noisy. These methods also yield a large number of diverse community structures as solutions, which is problematic for applications that impose constraints on the acceptable solutions or in cases where the user is focused on specific communities of interest. To address both of these problems, we develop a semi-supervised spin-glass model that enables current community detection methods to incorporate background knowledge in the forms of individual labels and pairwise constraints. Unlike current methods, our approach shows robust performance in the presence of noise in the relational network, and the ability to guide the discovery process toward specific community structures. We evaluate our algorithm on several benchmark networks and a new political sentiment network representing cooperative events between nations that was mined from news articles over six years.

Community detection in social and biological networks using differential evolution

Abstract: The community detection in complex networks is an important problem in many scientific fields, from biology to sociology. This paper proposes a new algorithm, Differential Evolution based Community Detection (DECD), which employs a novel optimization algorithm, differential evolution (DE) for detecting communities in complex networks. DE uses network modularity as the fitness function to search for an optimal partition of a network. Based on the standard DE crossover operator, we design a modified binomial crossover to effectively transmit some important information about the community structure in evolution. Moreover, a biased initialization process and a clean-up operation are employed in DECD to improve the quality of individuals in the population. One of the distinct merits of DECD is that, unlike many other community detection algorithms, DECD does not require any prior knowledge about the community structure, which is particularly useful for its application to real-world complex networks where prior knowledge is usually not available. We evaluate DECD on several artificial and real-world social and biological networks. Experimental results show that DECD has very competitive performance compared with other state-of-the-art community detection algorithms.