Network theory

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

Traversing Graphs: The Eulerian and Hamiltonian Theme

Abstract: This chapter deals with basic graph theoretical concepts and then focuses on special topics which are — in their applications — of relevance to theoretical and practical problems in OR. Therefore, this chapter is structured as follows: 1. Basics of Graph Theory. 2. Connectivity, Menger’s Theorem, the Splitting Lemma, and Factors. 3. Eulerian Graphs and Covering Walks, Cycle Decompositions and Cycle Covers. 4. Hamiltonian Cycles and Vertex-Covering Walks. 5. Elements of Matching Theory. 6. The Chinese Postman Problem, The Traveling Salesman Problem, and Related Problems. 7. Elements of Network Theory.

Centrality maps and the analysis of city street networks

Abstract: Firstly introduced in social science, the notion of centrality has spread to the whole complex network science. A centrality is a measure that quantifies whether an element of a network is well served or not, easy to reach, necessary to cross. This article focuses on cities' street network (seen as a communication network). We redefine two classical centralities (the closeness and the straightness) and introduce the notion of simplest centrality. To this we introduce a mathematical framework which allows considering a city as a geometrical continuum rather than a plain topological graph. The color plotting of the various centralities permits a visual analysis of the city and to diagnose local malfunctionings. The relevance of our framework and centralities is discussed from visual analysis of French towns and from computational complexity.

Multi-layered network structure: Relationship between financial and macroeconomic dynamics

Abstract: We demonstrate using multi-layered networks, the existence of an empirical linkage between the dynamics of the financial network constructed from the market indices and the macroeconomic networks constructed from macroeconomic variables such as trade, foreign direct investments, etc. for several countries across the globe. The temporal scales of the dynamics of the financial variables and the macroeconomic fundamentals are very different, which make the empirical linkage even more interesting and significant. Also, we find that there exist in the respective networks, core-periphery structures (determined through centrality measures) that are composed of similar set of countries—a result that may be related through the ‘gravity model’ of the country-level macroeconomic networks. Thus, from a multi-lateral openness perspective, we elucidate that for individual countries, larger trade connectivity is positively associated with higher financial return correlations. Furthermore, we show that the Economic Complexity Index and the equity markets have a positive relationship among themselves, as is the case for Gross Domestic Product. The data science methodology using network theory, coupled with standard econometric techniques constitute a new approach to studying multi-level economic phenomena in a comprehensive manner.

Modeling air traffic controllers' decision making processes with relational complexity network

Abstract: Quantifying the link between aircraft interaction complexity and the decision making process of air traffic controllers can help in developing sound cognitive models and effective intelligent supportive tools In this paper, the authors introduced a new relational complexity network framework derived from network theory and cognitive mechanisms to explain some key aspects in the decisional processes of air traffic control tasks In the validating experiment, the authors manipulated different aircraft interaction patterns and found that controllers' workload ranking, conflict detection rate, intervention decision and task completion time were significantly influenced by positions of single aircraft or aircraft pairs in the relational complexity network Theoretical and practical contributions are discussed