Showing papers on "Network science published in 2010"

Networks: An Introduction

Abstract: The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas. Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.

Social and Economic Networks

Abstract: Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. The many aspects of our lives that are governed by social networks make it critical to understand how they impact behavior, which network structures are likely to emerge in a society, and why we organize ourselves as we do. In Social and Economic Networks, Matthew Jackson offers a comprehensive introduction to social and economic networks, drawing on the latest findings in economics, sociology, computer science, physics, and mathematics. He provides empirical background on networks and the regularities that they exhibit, and discusses random graph-based models and strategic models of network formation. He helps readers to understand behavior in networked societies, with a detailed analysis of learning and diffusion in networks, decision making by individuals who are influenced by their social neighbors, game theory and markets on networks, and a host of related subjects. Jackson also describes the varied statistical and modeling techniques used to analyze social networks. Each chapter includes exercises to aid students in their analysis of how networks function. This book is an indispensable resource for students and researchers in economics, mathematics, physics, sociology, and business.

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

Abstract: Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows studies of community structure in a general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.

Networks of the Brain

Abstract: Over the last decade, the study of complex networks has expanded across diverse scientific fields. Increasingly, science is concerned with the structure, behavior, and evolution of complex systems ranging from cells to ecosystems. Modern network approaches are beginning to reveal fundamental principles of brain architecture and function, and in Networks of the Brain, Olaf Sporns describes how the integrative nature of brain function can be illuminated from a complex network perspective. Highlighting the many emerging points of contact between neuroscience and network science, the book serves to introduce network theory to neuroscientists and neuroscience to those working on theoretical network models. Brain networks span the microscale of individual cells and synapses and the macroscale of cognitive systems and embodied cognition. Sporns emphasizes how networks connect levels of organization in the brain and how they link structure to function. In order to keep the book accessible and focused on the relevance to neuroscience of network approaches, he offers an informal and nonmathematical treatment of the subject. After describing the basic concepts of network theory and the fundamentals of brain connectivity, Sporns discusses how network approaches can reveal principles of brain architecture. He describes new links between network anatomy and function and investigates how networks shape complex brain dynamics and enable adaptive neural computation. The book documents the rapid pace of discovery and innovation while tracing the historical roots of the field. The study of brain connectivity has already opened new avenues of study in neuroscience. Networks of the Brain offers a synthesis of the sciences of complex networks and the brain that will be an essential foundation for future research.

A Survey of Statistical Network Models

Abstract: Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active "network community" and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online "networking communities" such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.

Complex Networks: Structure, Robustness and Function

Abstract: 1. Introduction Part I. Random Network Models: 2. The Erdos-Renyi models 3. Observations in real-world networks 4. Models for complex networks 5. Growing network models Part II. Structure and Robustness of Complex Networks: 6. Distances in scale-free networks - the ultra small world 7. Self-similarity in complex networks 8. Distances in geographically embedded networks 9. The network's structure - the generating function method 10. Percolation on complex networks 11. Structure of random directed networks - the bow tie 12. Introducing weights - bandwidth allocation and multimedia broadcasting Part III. Network Function - Dynamics and Applications: 13. Optimization of the network structure 14. Epidemiological models 15. Immunization 16. Thermodynamic models on networks 17. Spectral properties, transport, diffusion and dynamics 18. Searching in networks 19. Biological networks and network motifs Part IV. Appendices References Index.

Information Contagion: an Empirical Study of the Spread of News on Digg and Twitter Social Networks

Abstract: Social networks have emerged as a critical factor in information dissemination, search, marketing, expertise and influence discovery, and potentially an important tool for mobilizing people. Social media has made social networks ubiquitous, and also given researchers access to massive quantities of data for empirical analysis. These data sets offer a rich source of evidence for studying dynamics of individual and group behavior, the structure of networks and global patterns of the flow of information on them. However, in most previous studies, the structure of the underlying networks was not directly visible but had to be inferred from the flow of information from one individual to another. As a result, we do not yet understand dynamics of information spread on networks or how the structure of the network affects it. We address this gap by analyzing data from two popular social news sites. Specifically, we extract social networks of active users on Digg and Twitter, and track how interest in news stories spreads among them. We show that social networks play a crucial role in the spread of information on these sites, and that network structure affects dynamics of information flow.

Graph Spectra for Complex Networks

Abstract: Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

Social Network Analysis: An Introduction 1

Abstract: Social network analysis takes as its starting point the premise that social life is created primarily and most importantly by relations and the patterns formed by these relations. Social networks are formally defined as a set of nodes (or network members) that are tied by one or more types of relations (Wasserman and Faust, 1994). Because network analysts take these networks as the primary building blocks of the social world, they not only collect unique types of data, they begin their analyses from a fundamentally different perspective than that adopted by individualist or attribute-based social science.

The complexity and robustness of metro networks

Abstract: Transportation systems, being real-life examples of networks, are particularly interesting to analyze from the viewpoint of the new and rapidly emerging field of network science. Two particular concepts seem to be particularly relevant: scale-free patterns and small-worlds. By looking at 33 metro systems in the world, this paper adapts network science methodologies to the transportation literature, and offers one application to the robustness of metros; here, metro refers to urban rail transit with exclusive right-of-way, whether it is underground, at grade or elevated. We find that most metros are indeed scale-free (with scaling factors ranging from 2.10 to 5.52) and small-worlds; they show atypical behaviors, however, with increasing size. In particular, the presence of transfer-hubs (stations hosting more than three lines) results in relatively large scaling factors. The analysis provides insights/recommendations for increasing the robustness of metro networks. Smaller networks should focus on creating transfer stations, thus generating cycles to offer alternative routes. For larger networks, few stations seem to detain a certain monopole on transferring, it is therefore important to create additional transfers, possibly at the periphery of city centers; the Tokyo system seems to remarkably incorporate these properties.

Modeling social networks from sampled data.

Abstract: Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of networks whose nodes represent individual social actors and whose edges represent a specified relationship between the actors. Most inference for social network models assumes that the presence or absence of all possible links is observed, that the information is completely reliable, and that there are no measurement (e.g., recording) errors. This is clearly not true in practice, as much network data is collected though sample surveys. In addition even if a census of a population is attempted, individuals and links between individuals are missed (i.e., do not appear in the recorded data). In this paper we develop the conceptual and computational theory for inference based on sampled network information. We first review forms of network sampling designs used in practice. We consider inference from the likelihood framework, and develop a typology of network data that reflects their treatment within this frame. We then develop inference for social network models based on information from adaptive network designs. We motivate and illustrate these ideas by analyzing the effect of link-tracing sampling designs on a collaboration network.

Network Properties Revealed through Matrix Functions

Abstract: The emerging field of network science deals with the tasks of modeling, comparing, and summarizing large data sets that describe complex interactions. Because pairwise affinity data can be stored in a two-dimensional array, graph theory and applied linear algebra provide extremely useful tools. Here, we focus on the general concepts of centrality, communicability, and betweenness, each of which quantifies important features in a network. Some recent work in the mathematical physics literature has shown that the exponential of a network's adjacency matrix can be used as the basis for defining and computing specific versions of these measures. We introduce here a general class of measures based on matrix functions, and show that a particular case involving a matrix resolvent arises naturally from graph-theoretic arguments. We also point out connections between these measures and the quantities typically computed when spectral methods are used for data mining tasks such as clustering and ordering. We finish with computational examples showing the new matrix resolvent version applied to real networks.

A New Measure of Centrality for Brain Networks

Abstract: Recent developments in network theory have allowed for the study of the structure and function of the human brain in terms of a network of interconnected components. Among the many nodes that form a network, some play a crucial role and are said to be central within the network structure. Central nodes may be identified via centrality metrics, with degree, betweenness, and eigenvector centrality being three of the most popular measures. Degree identifies the most connected nodes, whereas betweenness centrality identifies those located on the most traveled paths. Eigenvector centrality considers nodes connected to other high degree nodes as highly central. In the work presented here, we propose a new centrality metric called leverage centrality that considers the extent of connectivity of a node relative to the connectivity of its neighbors. The leverage centrality of a node in a network is determined by the extent to which its immediate neighbors rely on that node for information. Although similar in concept, there are essential differences between eigenvector and leverage centrality that are discussed in this manuscript. Degree, betweenness, eigenvector, and leverage centrality were compared using functional brain networks generated from healthy volunteers. Functional cartography was also used to identify neighborhood hubs (nodes with high degree within a network neighborhood). Provincial hubs provide structure within the local community, and connector hubs mediate connections between multiple communities. Leverage proved to yield information that was not captured by degree, betweenness, or eigenvector centrality and was more accurate at identifying neighborhood hubs. We propose that this metric may be able to identify critical nodes that are highly influential within the network.

Detecting sources of computer viruses in networks: theory and experiment

Abstract: We provide a systematic study of the problem of finding the source of a computer virus in a network. We model virus spreading in a network with a variant of the popular SIR model and then construct an estimator for the virus source. This estimator is based upon a novel combinatorial quantity which we term rumor centrality. We establish that this is an ML estimator for a class of graphs. We find the following surprising threshold phenomenon: on trees which grow faster than a line, the estimator always has non-trivial detection probability, whereas on trees that grow like a line, the detection probability will go to 0 as the network grows. Simulations performed on synthetic networks such as the popular small-world and scale-free networks, and on real networks such as an internet AS network and the U.S. electric power grid network, show that the estimator either finds the source exactly or within a few hops in different network topologies. We compare rumor centrality to another common network centrality notion known as distance centrality. We prove that on trees, the rumor center and distance center are equivalent, but on general networks, they may differ. Indeed, simulations show that rumor centrality outperforms distance centrality in finding virus sources in networks which are not tree-like.

Multiplicative Attribute Graph Model of Real-World Networks

Abstract: Large scale real-world network data such as social and information networks are ubiquitous. The study of such networks seeks to find patterns and explain their emergence through tractable models. In most networks, and especially in social networks, nodes have a rich set of attributes associated with them. We present the Multiplicative Attribute Graphs (MAG) model, which naturally captures the interactions between the network structure and the node attributes. We consider a model where each node has a vector of categorical latent attributes associated with it. The probability of an edge between a pair of nodes depends on the product of individual attribute-attribute similarities. The model yields itself to mathematical analysis. We derive thresholds for the connectivity and the emergence of the giant connected component, and show that the model gives rise to networks with a constant diameter. We also show that MAG model can produce networks with either log-normal or power-law degree distributions.

DivRank: the interplay of prestige and diversity in information networks

Abstract: Information networks are widely used to characterize the relationships between data items such as text documents. Many important retrieval and mining tasks rely on ranking the data items based on their centrality or prestige in the network. Beyond prestige, diversity has been recognized as a crucial objective in ranking, aiming at providing a non-redundant and high coverage piece of information in the top ranked results. Nevertheless, existing network-based ranking approaches either disregard the concern of diversity, or handle it with non-optimized heuristics, usually based on greedy vertex selection. We propose a novel ranking algorithm, DivRank, based on a reinforced random walk in an information network. This model automatically balances the prestige and the diversity of the top ranked vertices in a principled way. DivRank not only has a clear optimization explanation, but also well connects to classical models in mathematics and network science. We evaluate DivRank using empirical experiments on three different networks as well as a text summarization task. DivRank outperforms existing network-based ranking methods in terms of enhancing diversity in prestige.

Cold start link prediction

Abstract: In the traditional link prediction problem, a snapshot of a social network is used as a starting point to predict, by means of graph-theoretic measures, the links that are likely to appear in the future. In this paper, we introduce cold start link prediction as the problem of predicting the structure of a social network when the network itself is totally missing while some other information regarding the nodes is available. We propose a two-phase method based on the bootstrap probabilistic graph. The first phase generates an implicit social network under the form of a probabilistic graph. The second phase applies probabilistic graph-based measures to produce the final prediction. We assess our method empirically over a large data collection obtained from Flickr, using interest groups as the initial information. The experiments confirm the effectiveness of our approach.

Electrical centrality measures for electric power grid vulnerability analysis

Abstract: Centrality measures are used in network science to rank the relative importance of nodes and edges of a graph. Here we define new measures of centrality for power grid structure that are based on its functionality. We show that the relative importance analysis based on centrality in graph theory can be generalized to power grid network with its electrical parameters taken into account. In the paper we experiment with the proposed electrical centrality measures on the NYISO-2935 system and the IEEE 300-bus system. We analyze the centrality distribution in order to identify important nodes or branches in the system which are of essential importance in terms of system vulnerability. We also present and discuss a number of interesting discoveries regarding the importance rank of power grid nodes and branches.

Connecting the dots: towards archaeological network analysis

Abstract: In recent years network analysis has been applied in archaeological research to examine the structure of archaeological relationships of whatever sort. However, these archaeological applications share a number of issues concerning 1) the role of archaeological data in networks; 2) the diversity of network structures, their consequences and their interpretation; 3) the critical use of quantitative tools; and 4) the influence of other disciplines, especially sociology. This article concerns a deconstruction of past archaeological methods for examining networks. Through a case study of Roman table wares in the eastern Mediterranean, the article highlights a number of issues with network analysis as a method for archaeology. It urges caution regarding the uncritical application of network analysis methods developed in other disciplines and applied to archaeology. However, it stresses the potential benefits of network analysis for the archaeological discipline and acknowledges the need for specifically archaeological network analysis, which should be based on relational thinking and can be expanded with an archaeological toolset for quantitative analysis

Learning and Predicting the Evolution of Social Networks

Abstract: With the increasing availability of large social network data, there is also an increasing interest in analyzing how those networks evolve over time. Traditionally, the analysis of social networks has focused only on a single snapshot of a network. Researchers have already verified that social networks follow power-law degree distribution, have a small diameter, and exhibit small-world structure and community structure. Attempts to explain the properties of social networks have led to dynamic models inspired by the preferential attachment models which assumes that new network nodes have a higher probability of forming links with high-degree nodes, creating a rich-get-richer effect. Although some effort has been devoted to analyzing global properties of social network evolution, not much has been done to study graph evolution at a microscopic level. A first step in this direction investigated a variety of network formation strategies, showing that edge locality plays a critical role in network evolution. We propose a different approach. Following the paradigm of association rules and frequent-pattern mining, our work searches for typical patterns of structural changes in dynamic networks. Mining for such local patterns is a computationally challenging task that can provide further insight into the increasing amount of evolving network data. Beyond the notion of graph evolution rules (GERs), a concept that we introduced in an earlier work, we developed the Graph Evolution Rule Miner (GERM) software to extract such rules and applied these rules to predict future network evolution.

Graph mining applications to social network analysis

Abstract: The prosperity of Web 2.0 and social media brings about many diverse social networks of unprecedented scales, which present new challenges for more effec- tive graph-mining techniques. In this chapter, we present some graph patterns that are commonly observed in large-scale social networks. As most networks demonstrate strong community structures, one basic task in social network anal- ysis is community detection which uncovers the group membership of actors in a network. We categorize and survey representative graph mining approaches and evaluation strategies for community detection. We then present and discuss some research issues for future exploration.

Ambiguities in recurrence-based complex network representations of time series.

Abstract: Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail. We discuss the main requirements that permit a feasible system-theoretic interpretation of network topology in terms of dynamically invariant phase-space properties. Possible artifacts induced by disregarding these requirements are pointed out and systematically studied. Finally, a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed.

Behavioral dynamics and influence in networked coloring and consensus

Abstract: We report on human-subject experiments on the problems of coloring (a social differentiation task) and consensus (a social agreement task) in a networked setting. Both tasks can be viewed as coordination games, and despite their cognitive similarity, we find that within a parameterized family of social networks, network structure elicits opposing behavioral effects in the two problems, with increased long-distance connectivity making consensus easier for subjects and coloring harder. We investigate the influence that subjects have on their network neighbors and the collective outcome, and find that it varies considerably, beyond what can be explained by network position alone. We also find strong correlations between influence and other features of individual subject behavior. In contrast to much of the recent research in network science, which often emphasizes network topology out of the context of any specific problem and places primacy on network position, our findings highlight the potential importance of the details of tasks and individuals in social networks.

Mapping library and information science in China: a coauthorship network analysis

Abstract: This paper aims to identify the collaboration pattern and network structure of the coauthorship network of library and information science (LIS) in China. Using data from 18 core source LIS journals in China covering 6 years, we construct the LIS coau- thorship network. We analyze the network from both macro and micro perspectives and identify some key features of this network: this network is a small-world network, and follows the scale-free character. In the micro-level, we calculate each author's centrality values and compare them with citation counts. We find that centrality rankings are highly correlated with citation rankings. We also discuss the limitation of current centrality measures for coauthorship network analysis.

Identifying influential spreaders in complex networks

Abstract: Networks portray a multitude of interactions through which people meet, ideas are spread, and infectious diseases propagate within a society. Identifying the most efficient "spreaders" in a network is an important step to optimize the use of available resources and ensure the more efficient spread of information. Here we show that, in contrast to common belief, the most influential spreaders in a social network do not correspond to the best connected people or to the most central people (high betweenness centrality). Instead, we find: (i) The most efficient spreaders are those located within the core of the network as identified by the k-shell decomposition analysis. (ii) When multiple spreaders are considered simultaneously, the distance between them becomes the crucial parameter that determines the extend of the spreading. Furthermore, we find that-- in the case of infections that do not confer immunity on recovered individuals-- the infection persists in the high k-shell layers of the network under conditions where hubs may not be able to preserve the infection. Our analysis provides a plausible route for an optimal design of efficient dissemination strategies.

Centrality metric for dynamic networks

Abstract: Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to static networks. Most networks, on the other hand, are dynamic in nature, evolving over time through the addition or deletion of nodes and edges. A popular approach to analyzing such networks represents them by a static network that aggregates all edges observed over some time period. This approach, however, under or overestimates centrality of some nodes. We address this problem by introducing a novel centrality metric for dynamic network analysis. This metric exploits an intuition that in order for one node in a dynamic network to influence another over some period of time, there must exist a path that connects the source and destination nodes through intermediaries at different times. We demonstrate on an example network that the proposed metric leads to a very different ranking than analysis of an equivalent static network. We use dynamic centrality to study a dynamic citations network and contrast results to those reached by static network analysis.