Network theory

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

Using global modeling to unveil hidden couplings in small network motifs

Abstract: One of the main tasks in network theory is to infer relations among interacting elements. We propose global modeling as a tool to detect links between nodes and their nature. Various situations using small network motifs are investigated under the assumption that the variable to be measured at each node provides full observability when isolated. Such a choice ensures no intrinsic difficulties for getting a global model in the coupled situation. As a first step toward unveiling the coupling function in larger network motifs, we consider three different scenarios involving Rossler systems diffusively coupled, in a couple or embedded in a network, or parametrically forced. We show that the global modeling is able to determine not only the existence of an interaction but also its functional form, to retrieve the dynamics of the whole system, and to extract the equations governing the single node dynamics as if it was isolated.

Mapping WordNet to a relational network

Abstract: This paper discusses the implementation of a lexical knowledge base, based on a conceptualization of the problem domain in terms of relational network notation. In particular, we focus here on the importing of lemmas as instances from WordNet 2.0 into the knowledge base. Relational network notation (RNN) offers a simple yet powerful means for representing lexicogrammatical, semantic and sememic information. RNN is driven by relational network theory and incorporates developments in the theory which have been shown to not only describe but also explain linguistic phenomena in a neurologically plausible manner.

Transitions in random graphs of fixed degrees with many short cycles

Abstract: We analyze maximum entropy random graph ensembles with constrained degrees, drawn from arbitrary degree distributions, and a tuneable number of three-cycles (triangles). We find that such ensembles generally exhibit two transitions, a clustering and a shattering transition, separating three distinct regimes. At the clustering transition, the graphs change from typically having only isolated cycles to forming cycle clusters. At the shattering transition the graphs break up into many small cliques to achieve the desired three-cycle density. The locations of both transitions depend nontrivially on the system size. We derive a general formula for the three-cycle density in the regime of isolated cycles, for graphs with degree distributions that have finite first and second moments. For bounded degree distributions we present further analytical results on cycle densities and phase transition locations, which, while non-rigorous, are all validated via MCMC sampling simulations. We show that the shattering transition is of an entropic nature, occurring for all three-cycle density values, provided the system is large enough.

Emergence of global network property based on multi-agent voting model

Abstract: Recent studies have shown that various models can explain the emergence of complex networks, such as scale-free and small-world networks. This paper presents a different model to generate complex networks using a multi-agent approach. Each node is considered as an agent. Based on voting by all agents, edges are added repeatedly. We use four different kinds of centrality measures as a utility functions for agents. Depending on the centrality measure, the resultant networks differ considerably: typically, closeness centrality generates a scale-free network, degree centrality produces a random graph, betweenness centrality favors a regular graph, and eigenvector centrality brings a complete subgraph. The importance of the network structure among agents is widely noted in the multi-agent research literature. This paper contributes new insights into the connection between agents' local behavior and the global property of the network structure. We describe a detailed analysis on why these structures emerge, and present a discussion of the possible expansion and application of the model.

Just how small is this world really? An application of small world theory to the study of globalization

Abstract: Inspired by recent research on the dynamics of ‘small-world’ networks, in this article I apply its basic arguments and findings to the study of integrative processes in the international system. Employing the logic of network models we can learn, by analogy, from fields as diverse as neural science and forest fire prevention, much about the likely changes caused in the international political environment by increased interaction among its various units. I first explain recent developments in network theory and demonstrate their relevance for the study of international politics and economics. I then develop the most important insights to be transferred from network theory to the study of globalization. Network theory suggests that our world truly ‘shrinks’ only to the extent that relations among international actors cross pre-existing alliances or cooperative arrangements. Making the world a single place seems to require flexibility in forming attachments with other actors which goes beyond culturally and historically justified efforts at exchange and cooperation.