Network theory

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

Further Steps Towards a Logic of Polarization in Social Networks

Abstract: In this paper we look at different ways of modally defining properties related to the concept of balance in signed social networks where relations can be either positive or negative. The motivation is to be able to formally reason about the social phenomenon of group polarization, for which balance theory forms a network-theoretical underpinning. The starting point is a recently developed basic modal logic that axiomatizes the class of social networks that are balanced up to a certain degree. This property is not modally definable but can be captured using a deduction rule. In this paper we examine different possibilities for extending this basic language, in order to, first, be able to define frame properties such as balance and related properties such as non-overlapping positive and negative relations and collective connectedness as axioms, and, second, be able to define the property of full balance rather than balanced-up-to-a-degree. We consider extensions with both static modalities such as the universal and the difference modality, the intersection modality, and nominals known from hybrid logic, as well as dynamic global bridge modalities known from sabotage logic. Along the way we provide axioms for weak balance. Finally, to explore measures of how far a network is from polarization, we consider and compare variations of distance measures between models in relation to balance.

On topological approaches to network theory

Abstract: This paper covers network applications of topology, in particular linear graph theory. The first part is a review of developments, starting from Kirchhof and Maxwell, this leads to the second part in which are presented significant new results. The key items are: new techniques for treating active networks, generalization and extension of Wang algebra, and applications of linear graphs to multilevel maser analysis. A method for generation of explicit formulas for the number of trees in an undirected graph is illustrated. A new theorem is proved for such formulas when the graphs have uniform branch multiplicity. Examples of this concept are included.

Simplicial Models of Social Aggregation I

Abstract: This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a node, and every social interaction is represented by a segment connecting two nodes. Early work in family interactions, as well as more recent work in the study of terrorist organizations, shows that network modeling may be insufficient to describe the complexity of human social structures. Specifically, network theory does not seem to have enough flexibility to represent higher order aggregations, where several agents interact as a group, rather than as a collection of pairs. The model we present here uses a well established mathematical theory, the theory of simplicial complexes, to address this complex issue prevalent in interpersonal and intergroup communication. The theory enables us to provide a richer graphical representation of social interactions, and to determine quantitative mechanisms to describe the robustness of a social structure. We also propose a methodology to create random simplicial complexes, with the purpose of providing a new method to simulate computationally the creation and disgregation of social structures. Finally, we propose several measures which could be taken and observed in order to describe and study an actual social aggregation occurring in interpersonal and intergroup contexts.

A Survey of Network Theoretic Approaches for Risk Analysis of Complex Infrastructure Systems

Abstract: Many critical infrastructure systems are comprised of complex physical, geographical, and logical networks. Such systems include electric power, drinking water, wastewater, cellular communication, internet, and transportation. These systems are vulnerable to hazards, both natural (e.g. hurricanes and earthquakes) and man-made (e.g. terrorism and accidents), which can induce failures in network elements and reduce system performance. In conducting risk and reliability analyses for complex infrastructure systems, network theory has been used to understand the effect of perturbations of individual network elements on overall system performance. In this paper, we present a survey of research that has employed this network theoretic approach and provide a discussion of future research needs in the field.

Topology control for wireless mesh networks based on centrality metrics

Abstract: In this paper, a new mechanism for topology control in wireless mesh networks is proposed. We evaluate the application to this problem of the centrality metrics developed by social network analysts. Our target network is a wireless mesh network created by user hand-held devices. For this kind of networks, we aim to construct a connected dominating set that includes the most central nodes. Many advantages result from selecting just a subset of stations for routing tasks: reduction of collisions, protocol overhead, interference and energy consumption, better network organization and scalability. The resulting performance using the three most common centrality measures (degree, closeness and betweenness) is evaluated. As we are working with dynamic and decentralized networks, a distributed implementation is also proposed and evaluated.