Showing papers on "Network theory published in 2013"

Multilayer Networks

Abstract: In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others We also survey and discuss existing data sets that can be represented as multilayer networks We review attempts to generalize single-layer-network diagnostics to multilayer networks We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks We conclude with a summary and an outlook

Mathematical Formulation of Multilayer Networks

Abstract: A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing ‘‘traditional’’ network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.

Mathematical Formulation of Multi-Layer Networks

Abstract: A network representation is useful for describing the structure of a large variety of complex systems However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is very rich Achieving a deep understanding of such systems necessitates generalizing "traditional" network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks One must therefore develop a more general mathematical framework to cope with the challenges posed by multi-layer complex systems In this paper, we introduce a tensorial framework to study multi-layer networks, and we discuss the generalization of several important network descriptors and dynamical processes --including degree centrality, clustering coefficients, eigenvector centrality, modularity, Von Neumann entropy, and diffusion-- for this framework We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks Our tensorial approach will be helpful for tackling pressing problems in multi-layer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems

Topological Strata of Weighted Complex Networks.

Abstract: The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally defined quantities of nodes and edges, such as node degrees, edge weights and –more recently– correlations between neighboring nodes. However, statistical methods quickly become cumbersome when dealing with many-body properties and do not capture the precise mesoscopic structure of complex networks. Here we introduce a novel method, based on persistent homology, to detect particular non-local structures, akin to weighted holes within the link-weight network fabric, which are invisible to existing methods. Their properties divide weighted networks in two broad classes: one is characterized by small hierarchically nested holes, while the second displays larger and longer living inhomogeneities. These classes cannot be reduced to known local or quasilocal network properties, because of the intrinsic non-locality of homological properties, and thus yield a new classification built on high order coordination patterns. Our results show that topology can provide novel insights relevant for many-body interactions in social and spatial networks. Moreover, this new method creates the first bridge between network theory and algebraic topology, which will allow to import the toolset of algebraic methods to complex systems.

Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks

Abstract: A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Multi-layered interbank model for assessing systemic risk

Abstract: In this paper, we develop an agent-based multi-layered interbank network model based on a sample of large EU banks. The model allows for taking a more holistic approach to interbank contagion than is standard in the literature. A key finding of the paper is that there are non-negligible non-linearities in the propagation of shocks to individual banks when taking into account that banks are related to each other in various market segments. In a nutshell, the contagion effects when considering the shock propagation simultaneously across multiple layers of interbank networks can be substantially larger than the sum of the contagion-induced losses when considering the network layers individually. In addition, a bank "systemic importance" measure based on the multi-layered network model is developed and is shown to outperform standard network centrality indicators.

Community detection for correlation matrices

Abstract: A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that tends to be intrinsically biased due to its inconsistency with the null hypotheses underlying the existing algorithms. Here we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anti-correlated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested sub-communities with `hard' cores and `soft' peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy, detect `soft stocks' that alternate between communities, and discuss implications for portfolio optimization and risk management.

Identifying high betweenness centrality nodes in large social networks

Abstract: This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, κ-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high κ-path centrality have high node betweenness centrality. The randomized algorithm runs in time O(κ3 n 2−2αlog n) and outputs, for each vertex v, an estimate of its κ-path centrality up to additive error of ±n 1/2+α with probability 1 − 1/n 2. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared with existing randomized algorithms.

Hypernetworks in the Science of Complex Systems

Abstract: The modern world is complex beyond human understanding and control. The science of complex systems aims to find new ways of thinking about the many interconnected networks of interaction that defy traditional approaches. Thus far, research into networks has largely been restricted to pairwise relationships represented by links between two nodes.This volume marks a major extension of networks to multidimensional hypernetworks for modeling multi-element relationships, such as companies making up the stock market, the neighborhoods forming a city, people making up committees, divisions making up companies, computers making up the internet, men and machines making up armies, or robots working as teams. This volume makes an important contribution to the science of complex systems by: extending network theory to include dynamic relationships between many elements; providing a mathematical theory able to integrate multilevel dynamics in a coherent way; providing a new methodological approach to analyze complex systems; and, illustrating the theory with practical examples in the design, management and control of complex systems taken from many areas of application.

Knowledge, Networks and Space: Connectivity and the Problem of Non-Interactive Learning

Abstract: Gluckler J. Knowledge, networks and space: connectivity and the problem of non-interactive learning, Regional Studies. This paper develops an integrative perspective of network theory and economic geography to attain a more inclusive understanding of the creation and reproduction of knowledge. A sympathetic review of network research in the social sciences conveys that geography is often a marginalized factor and that the empirical evidence about its effect on networks and knowledge has been ambiguous. The paper criticizes network theory for its tendency to overlook processes of collective learning that happen outside networks. By conceptualizing non-interactive learning, it posits that an inclusive theory of knowledge has to integrate network accounts of interactions and geographical accounts of non-interactive learning. Gluckler J. 知识、网络与空间：连结性与非互动式学习的问题，区域研究。本文致力于发展网络理论与经济地理的整合性视角，以对知识的生产及创造做出更具包容性的理解。对于社会科学中网络研究的同情性回顾，传达了地理经常是被边缘化的因素，而地理对网络及知识所产生的影响之经验证据亦相当模煳。本文批判网络理论，因其有着忽略网络之外集体学习过程的倾向。透过概念化非互动式学习，本...

Incremental algorithm for updating betweenness centrality in dynamically growing networks

Abstract: The increasing availability of dynamically growing digital data that can be used for extracting social networks has led to an upsurge of interest in the analysis of dynamic social networks. One key aspect of social network analysis is to understand the central nodes in a network. However, dynamic calculation of centrality values for rapidly growing networks might be unfeasibly expensive, especially if it involves recalculation from scratch for each time period. This paper proposes an incremental algorithm that effectively updates betweenness centralities of nodes in dynamic social networks while avoiding re-computations by exploiting information from earlier computations. Our performance results suggest that our incremental betweenness algorithm can achieve substantial performance speedup, on the order of thousands of times, over the state of the art, including the best-performing non-incremental betweenness algorithm and a recently proposed betweenness update algorithm.

Social Network Analysis with Applications

Abstract: A comprehensive introduction to social network analysis that hones in on basic centrality measures, social links, subgroup analysis, data sources, and more Written by military, industry, and business professionals, this book introduces readers to social network analysis, the new and emerging topic that has recently become of significant use for industry, management, law enforcement, and military practitioners for identifying both vulnerabilities and opportunities in collaborative networked organizations. Focusing on models and methods for the analysis of organizational risk, Social Network Analysis with Applications provides easily accessible, yet comprehensive coverage of network basics, centrality measures, social link theory, subgroup analysis, relational algebra, data sources, and more. Examples of mathematical calculations and formulas for social network measures are also included. Along with practice problems and exercises, this easily accessible book covers: * The basic concepts of networks, nodes, links, adjacency matrices, and graphs * Mathematical calculations and exercises for centrality, the basic measures of degree, betweenness, closeness, and eigenvector centralities * Graph-level measures, with a special focus on both the visual and numerical analysis of networks * Matrix algebra, outlining basic concepts such as matrix addition, subtraction, multiplication, and transpose and inverse calculations in linear algebra that are useful for developing networks from relational data * Meta-networks and relational algebra, social links, diffusion through networks, subgroup analysis, and more An excellent resource for practitioners in industry, management, law enforcement, and military intelligence who wish to learn and apply social network analysis to their respective fields, Social Network Analysis with Applications is also an ideal text for upper-level undergraduate and graduate level courses and workshops on the subject.

A bio-inspired methodology of identifying influential nodes in complex networks.

Abstract: How to identify influential nodes is a key issue in complex networks. The degree centrality is simple, but is incapable to reflect the global characteristics of networks. Betweenness centrality and closeness centrality do not consider the location of nodes in the networks, and semi-local centrality, leaderRank and pageRank approaches can be only applied in unweighted networks. In this paper, a bio-inspired centrality measure model is proposed, which combines the Physarum centrality with the K-shell index obtained by K-shell decomposition analysis, to identify influential nodes in weighted networks. Then, we use the Susceptible-Infected (SI) model to evaluate the performance. Examples and applications are given to demonstrate the adaptivity and efficiency of the proposed method. In addition, the results are compared with existing methods.

An automated approach to network features of protein structure ensembles

Abstract: Network theory applied to protein structures provides insights into numerous problems of biological relevance. The explosion in structural data available from PDB and simulations establishes a need to introduce a standalone-efficient program that assembles network concepts/parameters under one hood in an automated manner. Herein, we discuss the development/application of an exhaustive, user-friendly, standalone program package named PSN-Ensemble, which can handle structural ensembles generated through molecular dynamics (MD) simulation/NMR studies or from multiple X-ray structures. The novelty in network construction lies in the explicit consideration of side-chain interactions among amino acids. The program evaluates network parameters dealing with topological organization and long-range allosteric communication. The introduction of a flexible weighing scheme in terms of residue pairwise cross-correlation/interaction energy in PSN-Ensemble brings in dynamical/chemical knowledge into the network representation. Also, the results are mapped on a graphical display of the structure, allowing an easy access of network analysis to a general biological community. The potential of PSN-Ensemble toward examining structural ensemble is exemplified using MD trajectories of an ubiquitin-conjugating enzyme (UbcH5b). Furthermore, insights derived from network parameters evaluated using PSN-Ensemble for single-static structures of active/inactive states of β2-adrenergic receptor and the ternary tRNA complexes of tyrosyl tRNA synthetases (from organisms across kingdoms) are discussed. PSN-Ensemble is freely available from http://vishgraph.mbu.iisc.ernet.in/PSN-Ensemble/psn_index.html.

An algorithm for k-degree anonymity on large networks

Abstract: In this paper, we consider the problem of anonymization on large networks. There are some anonymization methods for networks, but most of them can not be applied on large networks because of their complexity. We present an algorithm for k-degree anonymity on large networks. Given a network G, we construct a k-degree anonymous network, G, by the minimum number of edge modifications. We devise a simple and efficient algorithm for solving this problem on large networks. Our algorithm uses univariate micro-aggregation to anonymize the degree sequence, and then it modifies the graph structure to meet the k-degree anonymous sequence. We apply our algorithm to a different large real datasets and demonstrate their efficiency and practical utility.

Node-weighted interacting network measures improve the representation of real-world complex systems

Abstract: Network theory provides a rich toolbox consisting of methods, measures, and models for studying the structure and dynamics of complex systems found in nature, society, or technology. Recently, it has been pointed out that many real-world complex systems are more adequately mapped by networks of interacting or interdependent networks, e.g., a power grid showing interdependency with a communication network. Additionally, in many real-world situations it is reasonable to include node weights into complex network statistics to reflect the varying size or importance of subsystems that are represented by nodes in the network of interest. E.g., nodes can represent vastly different surface area in climate networks, volume in brain networks or economic capacity in trade networks. In this letter, combining both ideas, we derive a novel class of statistical measures for analysing the structure of networks of interacting networks with heterogeneous node weights. Using a prototypical spatial network model, we show that the newly introduced node-weighted interacting network measures indeed provide an improved representation of the underlying system's properties as compared to their unweighted analogues. We apply our method to study the complex network structure of cross-boundary trade between European Union (EU) and non-EU countries finding that it provides important information on trade balance and economic robustness.

Incremental algorithms for closeness centrality

Abstract: Centrality metrics have shown to be highly correlated with the importance and loads of the nodes within the network traffic. In this work, we provide fast incremental algorithms for closeness centrality computation. Our algorithms efficiently compute the closeness centrality values upon changes in network topology, i.e., edge insertions and deletions. We show that the proposed techniques are efficient on many real-life networks, especially on small-world networks, which have a small diameter and spike-shaped shortest distance distribution. We experimentally validate the efficiency of our algorithms on large-scale networks and show that they can update the closeness centrality values of 1.2 million authors in the temporal DBLP-coauthorship network 460 times faster than it would take to recompute them from scratch.

A new approach to identify influential spreaders in complex networks

Abstract: In the research of the propagation model of complex network, it is of theoretical and practical significance to detect the most influential spreaders. Global metrics such as degree centrality, closeness centrality, betweenness centrality and K-shell centrality can be used to identify the influential spreaders. These approaches are simple but have low accuracy. We propose K-shell and Community centrality (KSC) model. This model considers not only the internal properties of nodes but also the external properties of nodes, such as the com-munity which these nodes belong to. The Susceptible-Infected-Recovered (SIR) model is used to evaluate the performance of KSC model. The experiment result shows that our method is better to identify the most influential nodes. This paper comes up with a new idea and method for the study in this field.

The Role of Ego Networks in Manufacturing Joint Venture Formations

Abstract: This paper develops a network theory based framework of manufacturing joint venture formations and provides an empirical test in the context of the automotive industry. Hypotheses are developed regarding the implications of the network structure for a firm’s partner selection in manufacturing joint ventures. The roles of network theory constructs such as ego network size, ego network density, and ego network betweenness centrality on new manufacturing joint venture formations are explored using a dynamic framework. A comprehensive time series panel dataset with 3,247,124 observations containing the joint venture information of 1,158 automotive firms collectively engaging in 589 manufacturing joint ventures over 19 years is utilized to test the hypotheses. Results provide strong empirical support for the role of network structure in equity based partnership formation. Specifically, ego network size and ego network betweenness centrality of both focal manufacturer and potential partner have significant effects on new manufacturing joint venture formations. Findings regarding the role of ego network density are mixed.

Incremental closeness centrality for dynamically changing social networks

Abstract: Automation of data collection using online resources has led to significant changes in traditional practices of social network analysis. Social network analysis has been an active research field for many decades; however, most of the early work employed very small datasets. In this paper, a number of issues with traditional practices of social network analysis in the context of dynamic, large-scale social networks are pointed out. Given the continuously evolving nature of modern online social networking, we postulate that social network analysis solutions based on incremental algorithms will become more important to address high computation times for large, streaming, over-time datasets. Incremental algorithms can benefit from early pruning by updating the affected parts only when an incremental update is made in the network. This paper provides an example of this case by demonstrating the design of an incremental closeness centrality algorithm that supports efficient computation of all-pairs of shortest paths and closeness centrality in dynamic social networks that are continuously updated by addition, removal, and modification of nodes and edges. Our results obtained on various synthetic and real-life datasets provide significant speedups over the most commonly used method of computing closeness centrality, suggesting that incremental algorithm design is a fruitful research area for social network analysts.

Using centrality of concept maps as a measure of problem space states in computer-supported collaborative problem solving

Abstract: Problem solving likely involves at least two broad stages, problem space representation and then problem solution (Newell and Simon, Human problem solving, 1972). The metric centrality that Freeman (Social Networks 1:215–239, 1978) implemented in social network analysis is offered here as a potential measure of both. This development research study applied centrality measures to reanalyze existing concept maps from a recent investigation (Engelmann and Hesse, Computer-Supported Collaborative Learning 5:299–319, 2010). Participants (N = 120) were randomly assigned to interdependent (i.e. hidden profiles) or non-interdependent conditions to work online in triads using CmapTools software to create a concept map in order to solve a problem scenario. The centrality values of these group-created concept maps agreed with the common relations count analysis used in that investigation and allowed for additional comparisons as well as analysis by multidimensional scaling. Specifically, the interdependent triad maps resembled the fully explicated problem space, while the non-interdependent triad maps mainly resembled the problem solution. The results demonstrate that centrality is a useful measure of knowledge structure contained in these team concept map artifacts that allows researchers to infer problem representation start and goal state transitions during problem solving.

Betweenness centrality: algorithms and implementations

Abstract: Betweenness centrality is an important metric in the study of social networks, and several algorithms for computing this metric exist in the literature. This paper makes three contributions. First, we show that the problem of computing betweenness centrality can be formulated abstractly in terms of a small set of operators that update the graph. Second, we show that existing parallel algorithms for computing betweenness centrality can be viewed as implementations of different schedules for these operators, permitting all these algorithms to be formulated in a single framework. Third, we derive a new asynchronous parallel algorithm for betweenness centrality that (i) works seamlessly for both weighted and unweighted graphs, (ii) can be applied to large graphs, and (iii) is able to extract large amounts of parallelism. We implemented this algorithm and compared it against a number of publicly available implementations of previous algorithms on two different multicore architectures. Our results show that the new algorithm is the best performing one in most cases, particularly for large graphs and large thread counts, and is always competitive against other algorithms.

A matrix analysis of different centrality measures.

Abstract: Node centrality measures including degree, eigenvector, Katz and subgraph centralities are analyzed for both undirected and directed networks. We show how parameter-dependent measures, such as Katz and subgraph centrality, can be "tuned" to interpolate between degree and eigenvector centrality, which appear as limiting cases of the other measures. We interpret our finding in terms of the local and global influence of a given node in the graph as measured by graph walks of different length through that node. Our analysis gives some guidance for the choice of parameters in Katz and subgraph centrality, and provides an explanation for the observed correlations between different centrality measures and for the stability exhibited by the ranking vectors for certain parameter ranges. The important role played by the spectral gap of the adjacency matrix is also highlighted.

Hybrid Centrality Measures for Binary and Weighted Networks

Abstract: Existing centrality measures for social network analysis suggest the importance of an actor and give consideration to actor’s given structural position in a network. These existing measures suggest specific attribute of an actor (i.e., popularity, accessibility, and brokerage behavior). In this study, we propose new hybrid centrality measures (i.e., Degree-Degree, Degree-Closeness and Degree-Betweenness), by combining existing measures (i.e., degree, closeness and betweenness) with a proposition to better understand the importance of actors in a given network. Generalized set of measures are also proposed for weighted networks. Our analysis of co-authorship networks dataset suggests significant correlation of our proposed new centrality measures (especially weighted networks) than traditional centrality measures with performance of the scholars. Thus, they are useful measures which can be used instead of traditional measures to show prominence of the actors in a network.

Terrorist Networks, Network Energy and Node Removal: A New Measure of Centrality Based on Laplacian Energy

Abstract: In this work we propose a centrality measure for networks, which we refer to as Laplacian centrality, that provides a general framework for the centrality of a vertex based on the idea that the importance (or centrality) of a vertex is related to the ability of the network to respond to the deactivation or removal of that vertex from the network. In particular, the Laplacian centrality of a vertex is defined as the relative drop of Laplacian energy caused by the deactivation of this vertex. The Laplacian energy of network G with n vertices is defined as , where is the eigenvalue of the Laplacian matrix of G. Other dynamics based measures such as that of Masuda and Kori and PageRank compute the importance of a node by analyzing the way paths pass through a node while our measure captures this information as well as the way these paths are “redistributed” when the node is deleted. The validity and robustness of this new measure are illustrated on two different terrorist social network data sets and 84 networks in James Moody’s Add Health in school friendship nomination data, and is compared with other standard centrality measures.