Network theory

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

Absorbing random-walk centrality: Theory and algorithms

Abstract: We study a new notion of graph centrality based on absorbing random walks. Given a graph $G=(V,E)$ and a set of query nodes $Q\subseteq V$, we aim to identify the $k$ most central nodes in $G$ with respect to $Q$. Specifically, we consider central nodes to be absorbing for random walks that start at the query nodes $Q$. The goal is to find the set of $k$ central nodes that minimizes the expected length of a random walk until absorption. The proposed measure, which we call $k$ absorbing random-walk centrality, favors diverse sets, as it is beneficial to place the $k$ absorbing nodes in different parts of the graph so as to "intercept" random walks that start from different query nodes. Although similar problem definitions have been considered in the literature, e.g., in information-retrieval settings where the goal is to diversify web-search results, in this paper we study the problem formally and prove some of its properties. We show that the problem is NP-hard, while the objective function is monotone and supermodular, implying that a greedy algorithm provides solutions with an approximation guarantee. On the other hand, the greedy algorithm involves expensive matrix operations that make it prohibitive to employ on large datasets. To confront this challenge, we develop more efficient algorithms based on spectral clustering and on personalized PageRank.

Structural convergence of web graph, social network and malaria network: an analytical framework for emerging web-hybrid search engine

Abstract: It is a well known truth that there is no malaria transmission without blood-sucking bites by mosquitoes. Since there is no blood-sucking without contacts, it follows that the contacts between human beings and mosquitoes can be exploited to generate contact networks. Active computational research in this area is geared at developing new frontiers in modelling malaria transmission through network theory and methods. Ongoing research in this area points to the fact that there are structural similarities between web graph, social network and malaria networks. It is the aim of this paper to explore the structural convergence and to exploit this to build a framework that will pave the way for developing web-hybrid search engines. Like the emergence of search engines revolutionised web research, it is expected that application of search engines in malaria research will make a tremendous impact in malaria control.

Container Seaports Connectivity: A “Concept” Analysis

Abstract: Ports stand as connection nodes of the global shipping transportation network and have become increasingly important in economic, social and demographic reasons. Seaports networks constitute the operational backbone of maritime trade and in extent of the contemporary globalized economy. Measuring their attractiveness as nodes in terms of connectivity has become a matter of crucial importance for managers and policy makers. The concept of connectivity is well-documented in the social network literature and to some extent, transportation engineering literature. The measurement of a port’s connectivity is challenging especially, as it cannot be observed directly through published statistics. Previous attempts to define port connectivity are based on different techniques; from ad hoc metrics to concentration methods and more recently to more complex network models. Whereas all these methods give some measures of connectivity, identifying a ports’ relative position, they are subject to specific limitations, omitting important characteristics of the liner shipping network (e.g. hub and spoke system) and thus concluding to misspecified results. Furthermore, due to the complexity of the network theory metrics and high data requirements, previous attempts also generally provide connectivity scores for a single year, without sufficient information to examine how a port’s location is changing over time. The present paper aims to accentuate the importance to measure a port’s relative position in the maritime network through an extensive analysis of what has been done until now. Underscoring and analyzing the limitations of previous studies, it redefines a port’s connectivity through a gravity-based approach.

Network Analysis of Biblical Texts

Abstract: This article presents examples of using Network Theory to analyse the text of the New Testament. We provide an introduction to the basic concepts of Network Theory and centrality measures in networks and suggest a simple method of creating word co-occurrence networks from passages. Special consideration is given to the psychological realism of the model in the context of the ancient Mediterranean world. Following a demonstration of the method on the first two verses of the Gospel of John, we compare multiple versions of a miracle story with the help of network analysis. The final part of the article demonstrates how the method can be extended to account for the knowledge of different readerships in the interpretation of the text.