Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

Dynamical Aspects of Interaction Networks

Abstract: A connection between dynamical systems and network theory is outlined based on a mapping of the dynamics into a discrete probabilistic process, whereby the phase space is partitioned into finite size cells. It is found that the connectivity patterns of networks generated by deterministic systems can be related to the indicators of the dynamics such as local Lyapunov exponents. The procedure is extended to networks generated by stochastic 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.

Cost-effective viral marketing for time-critical campaigns in large-scale social networks

Abstract: Online social networks (OSNs) have become one of the most effective channels for marketing and advertising. Since users are often influenced by their friends, “word-of-mouth” exchanges, so-called viral marketing, in social networks can be used to increase product adoption or widely spread content over the network. The common perception of viral marketing about being cheap, easy, and massively effective makes it an ideal replacement of traditional advertising. However, recent studies have revealed that the propagation often fades quickly within only few hops from the sources, counteracting the assumption on the self-perpetuating of influence considered in literature. With only limited influence propagation, is massively reaching customers via viral marketing still affordable? How do we economically spend more resources to increase the spreading speed? We investigate the cost-effective massive viral marketing problem, taking into the consideration the limited influence propagation. Both analytical analysis based on power-law network theory and numerical analysis demonstrate that the viral marketing might involve costly seeding. To minimize the seeding cost, we provide mathematical programming to find optimal seeding for medium-size networks and propose VirAds, an efficient algorithm, to tackle the problem on large-scale networks. VirAds guarantees a relative error bound of $O(1)$ from the optimal solutions in power-law networks and outperforms the greedy heuristics that realizes on the degree centrality. Moreover, we also show that, in general, approximating the optimal seeding within a ratio better than $O(\log n)$ is unlikely possible.

Algorithmic Aspects of Graph Connectivity

Abstract: Algorithmic Aspects of Graph Connectivity is the first comprehensive book on this central notion in graph and network theory, emphasizing its algorithmic aspects. Because of its wide applications in the fields of communication, transportation, and production, graph connectivity has made tremendous algorithmic progress under the influence of the theory of complexity and algorithms in modern computer science. The book contains various definitions of connectivity, including edge-connectivity and vertex-connectivity, and their ramifications, as well as related topics such as flows and cuts. The authors comprehensively discuss new concepts and algorithms that allow for quicker and more efficient computing, such as maximum adjacency ordering of vertices. Covering both basic definitions and advanced topics, this book can be used as a textbook in graduate courses in mathematical sciences, such as discrete mathematics, combinatorics, and operations research, and as a reference book for specialists in discrete mathematics and its applications.

Has a Network Theory of Organizational Behaviour Lived Up to its Promises?[1]

Abstract: The study of organizational networks has a long history in the social and behavioural sciences. On the micro side, anthropologists and psychologists studied interpersonal networks within organizations (e.g., Roethlisberger and Dickson, 1939). On the macro side, sociologists studied interlocking directorates (Allen, 1974; Levine, 1972), human service delivery systems (Aldrich, 1976; Rogers, 1974) and community power structures (Hunter, 1953; Laumann and Pappi, 1976; Perrucci and Pilisuk, 1970; Turk, 1977). Although management scholars had studied human service networks as well (e.g., Van de Ven, 1976), most credit Tichy et al. (1979) with introducing the topic of network analysis to the management literature. The institutionalization of the network approach in management circles is evident in the Academy of Management's 2002 meeting theme, 'Building Effective Networks' and special issues devoted to network analysis in the Academy of Management Journal (volume 47, issue 6, December 2004) and the Academy of Management Review (volume 31, issue, 3 July 2006). After all these years and hundreds of publications I think it is fair to ask: has a network perspective on organizational behaviour lived up to its promises? To spare you the suspense, my answer is yes — but we are not yet at the point where we have a single omnibus network theory of organizational behaviour or anything approaching universal laws of network organizations. Rather, as this essay will show, networks are key elements in several substantive theories of organizational behavior but rarely do they alone explain outcomes. Almost all effects are contingent upon context. On the empirical side, the evidence is fairly convincing that networks matter, i.e., network variables explain significant amounts of variance, but often research designs leave much to be desired, much of the work is descriptive, and we are not necessarily sure why or how networks matter. In this way, the views expressed in this essay are not unsympathetic to those expressed by Salancik (1995) in his classic critique of network theories of organization. The essay will be divided into four parts. First, I describe some of the ways that network analysis is more complicated than standard survey analysis. Secondly, I address the question: what role do network ideas play in network theories of organizational behaviour? Thirdly, I evaluate network theories and research