Showing papers on "Network theory published in 2011"

Temporal Networks

Abstract: A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems In many cases, however, the edges are not continuously active As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts In some cases, edges are active for non-negligible periods of time: eg, the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

On Network Theory

Abstract: Research on social networks has grown considerably in the last decade. However, there is a certain amount of confusion about network theory — for example, what it is, what is distinctive about it, and how to generate new theory. This paper attempts to remedy the situation by clarifying the fundamental concepts of the field (such as the network) and characterizing how network reasoning works. We start by considering the definition of network, noting some confusion caused by two different perspectives, which we refer to as realist and nominalist. We then analyze two well-known network theories, Granovetter’s strength of weak ties, to identify characteristic elements of network theorizing. We argue that both theories share an underlying theoretical model, which we label the network flow model, from which we derive additional implications. We also discuss network phenomena that do not appear to fit the flow model and discuss the possibility of a second fundamental model, which we call the bond model. We close with a discussion of the merits of model-based network theorizing for facilitating the generation of new theory, as well as a discussion of endogeneity in network theorizing.

On Network Theory

Abstract: Research on social networks has grown considerably in the last decade. However, there is a certain amount of confusion about network theory---for example, what it is, what is distinctive about it, and how to generate new theory. This paper attempts to remedy the situation by clarifying the fundamental concepts of the field (such as the network) and characterizing how network reasoning works. We start by considering the definition of network, noting some confusion caused by two different perspectives, which we refer to as realist and nominalist. We then analyze two well-known network theories, Granovetter's strength of weak ties theory [Granovetter, M. S. 1973. The strength of weak ties. Amer. J. Sociol.78(6) 1360--1380] and Burt's structural holes theory [Burt, R. S. 1992. Structural Holes: The Social Structure of Competition. Havard University Press, Cambridge, MA], to identify characteristic elements of network theorizing. We argue that both theories share an underlying theoretical model, which we label the network flow model, from which we derive additional implications. We also discuss network phenomena that do not appear to fit the flow model and discuss the possibility of a second fundamental model, which we call the bond model. We close with a discussion of the merits of model-based network theorizing for facilitating the generation of new theory, as well as a discussion of endogeneity in network theorizing.

Networks and the epidemiology of infectious disease.

Abstract: The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues.

Connectivity for conservation: a framework to classify network measures

Abstract: Graph theory, network theory, and circuit theory are increasingly being used to quantify multiple aspects of habitat connectivity and protected areas There has been an explosive proliferation of network (connectivity) measures, resulting in over 60 measures for ecologists to now choose from Conceptual clarification on the ecological meaning of these network measures and their interrelationships is overdue We present a framework that categorizes network measures based on the connectivity property that they quantify (ie, route-specific flux, route redundancy, route vulnerability, and connected habitat area) and the structural level of the habitat network to which they apply The framework reveals a lack of network measures in the categories of "route-specific flux among neighboring habitat patches" and "route redundancy at the level of network components" We propose that network motif and path redundancy measures can be developed to fill the gaps in these categories The value of this framework lies in its ability to inform the selection and application of network measures Ultimately, it will allow a better comparison among graph, network, and circuit analyses, which will improve the design and management of connected landscapes

Orchestration Processes in Network-Centric Innovation: Evidence From the Field

Abstract: Executive Overview Companies have increasingly shifted from innovation initiatives that are centered on internal resources to those that are centered on external networks (said another way, a shift from firm-centric innovation to network-centric innovation). In this paper, we combine insights from product development and network theory with evidence from an extensive field study to describe the nature of a hub firm's orchestration processes in network-centric innovation. Our analysis indicates that network orchestration processes reflect the interplay between elements of innovation design and network design. Promising directions for future research related to network-centric innovation are discussed.

A Network Theory of Power

Abstract: 1. Networking Power: the power of the actors and organizations included in the networks that constitute the core of the global network society over human collectives and individuals who are not included in these global networks. 2. Network Power: the power resulting from the standards required to coordinate social interaction in the networks. In this case, power is exercised not by exclusion from the networks but by the imposition of the rules of inclusion. 3. Networked Power: the power of social actors over other social actors in the network. The forms and processes of networked power are specific to each network. 4. Network-making Power: the power to program specific networks according to the interests and values of the programmers, and the power to switch different networks following the strategic alliances between the dominant actors of various networks. Counterpower is exercised in the network society by fighting to change the programs of specific networks and by the effort to disrupt the switches that reflect dominant interests and replace them with alternative switches between networks. Actors are humans, but humans are organized in networks. Human networks act on networks via the programming and switching of organizational networks. In the network society, power and counterpower aim fundamentally at influencing the neural networks in the human mind by using mass communication networks and mass self-communication networks.

Generalized Louvain method for community detection in large networks

Abstract: In this paper we present a novel strategy to discover the community structure of (possibly, large) networks This approach is based on the well-know concept of network modularity optimization To do so, our algorithm exploits a novel measure of edge centrality, based on the κ-paths This technique allows to efficiently compute a edge ranking in large networks in near linear time Once the centrality ranking is calculated, the algorithm computes the pairwise proximity between nodes of the network Finally, it discovers the community structure adopting a strategy inspired by the well-known state-of-the-art Louvain method (henceforth, LM), efficiently maximizing the network modularity The experiments we carried out show that our algorithm outperforms other techniques and slightly improves results of the original LM, providing reliable results Another advantage is that its adoption is naturally extended even to unweighted networks, differently with respect to the LM

Statistically Validated Networks in Bipartite Complex Systems

Abstract: Many complex systems present an intrinsic bipartite structure where elements of one set link to elements of the second set. In these complex systems, such as the system of actors and movies, elements of one set are qualitatively different than elements of the other set. The properties of these complex systems are typically investigated by constructing and analyzing a projected network on one of the two sets (for example the actor network or the movie network). Complex systems are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set, and this heterogeneity makes it very difficult to discriminate links of the projected network that are just reflecting system's heterogeneity from links relevant to unveil the properties of the system. Here we introduce an unsupervised method to statistically validate each link of a projected network against a null hypothesis that takes into account system heterogeneity. We apply the method to a biological, an economic and a social complex system. The method we propose is able to detect network structures which are very informative about the organization and specialization of the investigated systems, and identifies those relationships between elements of the projected network that cannot be explained simply by system heterogeneity. We also show that our method applies to bipartite systems in which different relationships might have different qualitative nature, generating statistically validated networks in which such difference is preserved.

Resilience enhancing expansion strategies for water distribution systems: A network theory approach

Abstract: Planners and engineers attempting to improve the resilience of water distribution systems face numerous challenges regarding the allocation and placement of redundancy so as to reduce the likelihood and impact of asset failures and take into consideration the growing demand for clean water, now and into the future. Water distribution systems may be represented as networks of multiple nodes (e.g. reservoirs, storage tanks and hydraulic junctions) interconnected by physical links (e.g. pipes) where the connectivity patterns of this network affects its reliability, efficiency and robustness to failures. In this paper we employ the link-node representation of water infrastructures and exploit a wide range of advanced and emerging network theory metrics and measurements to study the building blocks of the systems and quantify properties such as redundancy and fault tolerance, in order to establish relationships between structural features and performance of water distribution systems. We study the water distribution network of a growing city from a developing country and explore network expansion strategies that are aimed to secure and promote structural invulnerability, subject to design and budget constraints.

Investigating the topology of interacting networks - Theory and application to coupled climate subnetworks

Abstract: Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere’s three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere’s vertical stratification and general circulation. Specifically, the new measure “cross-betweenness” identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective.

Randomizing world trade. I. A binary network analysis

Abstract: The international trade network (ITN) has received renewed multidisciplinary interest due to recent advances in network theory. However, it is still unclear whether a network approach conveys additional, nontrivial information with respect to traditional international-economics analyses that describe world trade only in terms of local (first-order) properties. In this and in a companion paper, we employ a recently proposed randomization method to assess in detail the role that local properties have in shaping higher-order patterns of the ITN in all its possible representations (binary or weighted, directed or undirected, aggregated or disaggregated by commodity) and across several years. Here we show that, remarkably, the properties of all binary projections of the network can be completely traced back to the degree sequence, which is therefore maximally informative. Our results imply that explaining the observed degree sequence of the ITN, which has not received particular attention in economic theory, should instead become one the main focuses of models of trade.

Network Theory | Multidimensional Networks and the Dynamics of Sociomateriality: Bringing Technology Inside the Network

Abstract: This article explores the theoretical implications of developing multidimensional social networks that include nonhuman technological elements. Using ideas from actor-network theory and sociomateriality, we develop a typology for multidimensional networks that includes multiple kinds of nodes and multiple kinds of relations. This typology includes traditional types of nodes, like people, and traditional types of relations, like “shares information with,” along with types of nodes that are technological artifacts, like databases, and types of nonhuman relations, like embodiment. In this way, technology is moved inside the social network and becomes an inherent part of it. An illustrative case shows how the inclusion of nonhuman artifacts and relations in the networks of an automobile design firm significantly changes our understanding of the emergent dynamics in this sociomaterial network. These results are extended by an exploration of how to develop multidimensional, multitheoretical, and multilevel models that include technological artifacts and relations.

Beyond Shannon: the quest for fundamental performance limits of wireless ad hoc networks

Abstract: We describe a new theoretical framework for determining fundamental performance limits of wireless ad hoc networks. The framework expands the traditional definition of Shannon capacity to incorporate notions of delay and outage. Novel tools are described for upper and lower bounding the network performance regions associated with these metrics under a broad range of assumptions about channel and network dynamics, state information, and network topologies. We also develop a flexible and dynamic interface between network applications and the network performance regions to obtain the best end-to-end performance. Our proposed framework for determining performance limits of wireless networks embraces an interdisciplinary approach to this challenging problem that incorporates Shannon Theory along with network theory, combinatorics, optimization, stochastic control, and game theory. Preliminary results of this approach are described and promising future directions of research are outlined.

The semantic organization of the animal category: evidence from semantic verbal fluency and network theory

Abstract: Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life-specific experiences. How humans organize semantic information remains poorly understood. In an effort to better understand this issue, we conducted a verbal fluency experiment on 200 participants with the aim of inferring and representing the conceptual storage structure of the natural category of animals as a network. This was done by formulating a statistical framework for co-occurring concepts that aims to infer significant concept–concept associations and represent them as a graph. The resulting network was analyzed and enriched by means of a missing links recovery criterion based on modularity. Both network models were compared to a thresholded co-occurrence approach. They were evaluated using a random subset of verbal fluency tests and comparing the network outcomes (linked pairs are clustering transitions and disconnected pairs are switching transitions) to the outcomes of two expert human raters. Results show that the network models proposed in this study overcome a thresholded co-occurrence approach, and their outcomes are in high agreement with human evaluations. Finally, the interplay between conceptual structure and retrieval mechanisms is discussed.

Flow graphs: Interweaving dynamics and structure

Abstract: The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential because different dynamical processes may be affected very differently by network topology. A full characterization of such systems thus requires a formalization that encompasses both aspects simultaneously, rather than relying only on the topological adjacency matrix. To achieve this, we introduce the concept of flow graphs, namely weighted networks where dynamical flows are embedded into the link weights. Flow graphs provide an integrated representation of the structure and dynamics of the system, which can then be analyzed with standard tools from network theory. Conversely, a structural network feature of our choice can also be used as the basis for the construction of a flow graph that will then encompass a dynamics biased by such a feature. We illustrate the ideas by focusing on the mathematical properties of generic linear processes on complex networks that can be represented as biased random walks and their dual consensus dynamics, and show how our framework improves our understanding of these processes.

Networks in plant epidemiology: from genes to landscapes, countries, and continents.

Abstract: There is increasing use of networks in ecology and epidemiology, but still relatively little application in phytopathology. Networks are sets of elements (nodes) connected in various ways by links (edges). Network analysis aims to understand system dynamics and outcomes in relation to network characteristics. Many existing natural, social, and technological networks have been shown to have small-world (local connectivity with short-cuts) and scale-free (presence of super-connected nodes) properties. In this review, we discuss how network concepts can be applied in plant pathology from the molecular to the landscape and global level. Wherever disease spread occurs not just because of passive/natural dispersion but also due to artificial movements, it makes sense to superimpose realistic models of the trade in plants on spatially explicit models of epidemic development. We provide an example of an emerging pathosystem (Phytophthora ramorum) where a theoretical network approach has proven particularly fruitful in analyzing the spread of disease in the UK plant trade. These studies can help in assessing the future threat posed by similar emerging pathogens. Networks have much potential in plant epidemiology and should become part of the standard curriculum.

Centrality measures and thermodynamic formalism for complex networks.

Abstract: In the study of small and large networks it is customary to perform a simple random walk where the random walker jumps from one node to one of its neighbors with uniform probability. The properties of this random walk are intimately related to the combinatorial properties of the network. In this paper we propose to use the Ruelle-Bowens random walk instead, whose probability transitions are chosen in order to maximize the entropy rate of the walk on an unweighted graph. If the graph is weighted, then a free energy is optimized instead of the entropy rate. Specifically, we introduce a centrality measure for large networks, which is the stationary distribution attained by the Ruelle-Bowens random walk; we name it entropy rank. We introduce a more general version, which is able to deal with disconnected networks, under the name of free-energy rank. We compare the properties of those centrality measures with the classic PageRank and hyperlink-induced topic search (HITS) on both toy and real-life examples, in particular their robustness to small modifications of the network. We show that our centrality measures are more discriminating than PageRank, since they are able to distinguish clearly pages that PageRank regards as almost equally interesting, and are more sensitive to the medium-scale details of the graph.

Identifying Influential Nodes in Online Social Networks Using Principal Component Centrality

Abstract: Identifying the most influential nodes in social networks is a key problem in social network analysis. However, without a strict definition of centrality the notion of what constitutes a central node in a network changes with application and the type of commodity flowing through a network. In this paper we identify social hubs, nodes at the center of influential neighborhoods, in massive online social networks using principal component centrality (PCC). We compare PCC with eigenvector centrality's (EVC), the de facto measure of node influence by virtue of their position in a network. We demonstrate PCC's performance by processing a friendship graph of 70, 000 users of Google's Orkut social networking service and a gaming graph of 143, 020 users obtained from users of Facebook's 'Fighters Club' application.

K-path centrality: a new centrality measure in 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. Experimental evaluations on diverse real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared to known randomized algorithms.

Parameterized centrality metric for network analysis

Abstract: A variety of metrics have been proposed to measure the relative importance of nodes in a network. One of these, alpha-centrality [P. Bonacich, Am. J. Sociol. 92, 1170 (1987)], measures the number of attenuated paths that exist between nodes. We introduce a normalized version of this metric and use it to study network structure, for example, to rank nodes and find community structure of the network. Specifically, we extend the modularity-maximization method for community detection to use this metric as the measure of node connectivity. Normalized alpha-centrality is a powerful tool for network analysis, since it contains a tunable parameter that sets the length scale of interactions. Studying how rankings and discovered communities change when this parameter is varied allows us to identify locally and globally important nodes and structures. We apply the proposed metric to several benchmark networks and show that it leads to better insights into network structure than alternative metrics.

Network Theory| A Network Theory of Power

Abstract: Power in the network society is exercised through networks. There are four different forms of power under these social and technological conditions: 1. Networking Power: the power of the actors and organizations included in the networks that constitute the core of the global network society over human collectives and individuals who are not included in these global networks. 2. Network Power: the power resulting from the standards required to coordinate social interaction in the networks. In this case, power is exercised not by exclusion from the networks but by the imposition of the rules of inclusion. 3. Networked Power: the power of social actors over other social actors in the network. The forms and processes of networked power are specific to each network. 4. Network-making Power: the power to program specific networks according to the interests and values of the programmers, and the power to switch different networks following the strategic alliances between the dominant actors of various networks. Counterpower is exercised in the network society by fighting to change the programs of specific networks and by the effort to disrupt the switches that reflect dominant interests and replace them with alternative switches between networks. Actors are humans, but humans are organized in networks. Human networks act on networks via the programming and switching of organizational networks. In the network society, power and counterpower aim fundamentally at influencing the neural networks in the human mind by using mass communication networks and mass self-communication networks.

Network evolution based on centrality.

Abstract: We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arise under various centrality measures, and solve analytically the network evolution. During the complete evolution, the network is characterized by nestedness: the neighborhood of a node is contained in the neighborhood of the nodes with larger degree. We find a discontinuous transition in the network density between hierarchical and homogeneous networks, depending on the rate of link decay. We also show that this evolution mechanism leads to double power-law degree distributions, with interrelated exponents.

Look Who’s Linked With Whom: A Case Study of One Community Basketball Network

Abstract: The Canadian Sport Policy advocates for increased interaction among sport organizations as a means to create a more efficient and effective system. The purpose of this study was to explore the existence and nature of linkages among a network of community basketball providers. Network theory focuses on the interconnections of organizations by considering the structural, social, and economic bonds of cooperative behavior. Quantitative data were collected via a questionnaire and analyzed using network software UCINET 6 to assess the numbers and types of linkages among a network of community basketball organizations (n = 10) in one geographical region. Next, in-depth, semistructured interviews were conducted with leaders from the organizations and from their provincial/national governing bodies (n = 11) to assess the barriers to linkages among these organizations. Results indicated a loosely coupled network, wherein issues of power and dependence, uncertainty, and the lack of managerial structures to initiate...

Local Natural Connectivity in Complex Networks

Abstract: In network theory, a complex network represents a system whose evolving structure and dynamic behavior contribute to its robustness. The natural connectivity is recently proposed as a spectral measure to characterize the robustness of complex networks. We decompose the natural connectivity of a network as local natural connectivity of its connected components and quantify their contributions to the network robustness. In addition, we compare the natural connectivity of a network with that of an induced subgraph of it based on interlacing theorems. As an application, we derive an inequality for eigenvalues of Erdos-Renyi random graphs.