Network theory

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

A possibility of filling the gap between local and global passivity of non‐linear networks and some of its consequences

Abstract: In the qualitative theory of non-linear networks the non-linear n-ports are generally considered either locally passive or globally passive even eventually globally passive (the most restrictive or the least restrictive properties respectively). Moreover the reciprocity condition in many cases (e.g. complete stability) restricts the area of applications. In the area of economics and other fields, basically motivated by Sandberg's results, the role of the off-diagonally monotone and antitone mappings is crucial. In this paper, based on the above facts and results, it is shown that partly similar classes of mappings could have a role in non-linear network theory. More precisely, the off-diagonally locally active (passive) n-ports, defined in the paper, could represent an important new class of n-ports. As an application of the features of this new class of n-ports two Theorems are given showing conditions under which in case of a network consisting of off-diagonally locally active n-ports the DC solution can be uniquely calculated using the standard iterative methods and an autonomous network is asymptotically stable in a given domain. Hence, this paper partially overcomes the so called ‘curse of non-reciprocity’.

Application of neural networks in robotic control

Abstract: The application of the fuzzy neural-logic network theory to improve the performance of controlling a robot is explored. Neural-logic is a three-valued logic and as such it can represent many more logical variations than the two-valued Boolean logic, e.g., the neural-logic network can implement the logical 'NOT' operation, which is essential for logical inference. It is concluded that the performance of a robot using the fuzzy neural-logic network controller will be significantly improved because it can handle the logical 'DON'T KNOW' operations so that it provides not only the conventional pattern matching capability, but also the inferencing capability. >

Network theory applied to linguistics: new advances in language classification and typology

Abstract: This thesis bridges between two scientific fields -- linguistics and computer science -- in terms of Linguistic Networks. From the linguistic point of view we examine whether languages can be distinguished when looking at network topology of different linguistic networks. We deal with up to 17 languages and ask how far the methods of network theory reveal the peculiarities of single languages. We present and apply network models from different levels of linguistic representation: syntactic, phonological and morphological. The network models presented here allow to integrate various linguistic features at once, which enables a more abstract, holistic view at the particular language. From the point of view of computer science we elaborate the instrumentarium of network theory applying it to a new field. We study the expressiveness of different network features and their ability to characterize language structure. We evaluate the interplay of these features and their goodness in the task of classifying languages genealogically. Among others we compare network features related to: average degree, average geodesic distance, clustering, entropy-based indices, assortativity, centrality, compactness etc. We also propose some new indices that can serve as additional characteristics of networks. The results obtained show that network models succeed in classifying related languages, and allow to study language structure in general. The mathematical analysis of the particular network indices brings new insights into the nature of these indices and their potential when applied to different networks.

Numerical Investigation of Metrics for Epidemic Processes on Graphs (In Proceedings of 2015 Asilomar Conference on Signals, Systems, and Computers)

Abstract: This study develops the epidemic hitting time (EHT) metric on graphs measuring the expected time an epidemic starting at node a in a fully susceptible network takes to propagate and reach node b. An associated EHT centrality measure is then compared to degree, betweenness, spectral, and effective resistance centrality measures through exhaustive numerical simulations on several real-world network data-sets. We find two surprising observations: first, EHT centrality is highly correlated with effective resistance centrality; second, the EHT centrality measure is much more delocalized compared to degree and spectral centrality, highlighting the role of peripheral nodes in epidemic spreading on graphs. I. INTRODUCTION Dynamics on graphs has long been a central research topic across many applied disciplines. Several graph related quanti- ties have proven successful in studying different applications. In particular, the effective resistance metric appears to be an important tool for studying a variety of dynamics over graphs, including, but not limited to, random walks on graphs, electri- cal networks, Markov chains, and averaging networks (4). It comes as no surprise that effective resistance is important for all these dynamic processes because they are gradient driven processes. The effective resistance is closely related to the Laplacian matrix of the underlying graph. However, epidemic spreading dynamics is a branching process and behaves very differently from gradient driven dynamics. In this paper, we seek graph quantities that help describe epidemic dynamics. Centralities are frequently used to de- termine properties of the underlying topology of a network. In fact, comparing different centralities on the same network can be used to classify the network structure (22). Herein, we compare common centralities as well as graph metrics to see how to best understand epidemic dynamics. We use many of the same real-world data sets as in (22) and conclude that surprisingly, regardless of the underlying network structure, numerics indicate that the effective resistance is the most relevant graph quantity to the epidemic spreading. A partial explanation is offered at the end of the article.

Graph Theory, Social Network Analysis, and Network Science

Abstract: Network analysis provides a versatile framework for modeling complex systems and because of its universal applicability it has been invented and rediscovered in many different disciplines Each of these disciplines enriches the field by providing its own perspective and its own approaches; the three most prominent disciplines in the area are sociology , graph theory , and statistical physics As these disciplines follow very different aims, it is vital to understand the different approaches and perspectives This chapter elaborates and opposes the different approaches to highlight those points which are important for the topic of interest—network analysis literacy