Network theory

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

A quick and practicable power flow tracing method on electric energy market. I. Theoretic fundament

Abstract: In a competitive market environment, to "fairly allocate the total cost of transmission", which is identical with the actual utilization of the network, is most important Based on network theory and graph theorem, this paper theoretically proves and extends the proportional sharing principle With it, the employment of transmission lines by different generators and loads can be confirmed theoretically, while energy consumers can be impartially, rationally charged, and quickly and truly ascertained according to the actual utilization of the network Also based on this principle, many problems in the electricity energy market field can be settled

Association and Centrality in Criminal Networks

Abstract: Network-based techniques are widely used in criminal investigations because patterns of association are actionable and understandable. Existing network models with nodes as first class entities and their related measures (e.g., social networks and centrality measures) are unable to capture and analyze the structural richness required to model and investigate criminal network entities and their associations. We demonstrate a need to rethink entity associations with one specific case (inspired by \textit{The Wire}, a tv series about organized crime in Baltimore, United States) and corroborated by similar evidence from other cases. Our goal is to develop centrality measures for fragmented and non-navigational states of criminal network investigations. A network model with three basic first class entities is presented together with a topology of associations between network entities. We implement three of these associations and extend and test two centrality measures using Crime Fighter Investigator, a novel tool for criminal network investigation. Our findings show that the extended centrality measures offer new insights into criminal networks.

Fast Exact and Approximate Computation of Betweenness Centrality in Social Networks

Abstract: Social networks have demonstrated in the last few years to be a powerful and flexible concept useful to represent and analyze data emerging from social interactions and social activities. The study of these networks can thus provide a deeper understanding of many emergent global phenomena. The amount of data available in the form of social networks is growing by the day. This poses many computational challenging problems for their analysis. In fact many analysis tools suitable to analyze small to medium sized networks are inefficient for large social networks. The computation of the betweenness centrality index (BC) is a well established method for network data analysis and it is also important as subroutine in more advanced algorithms, such as the Girvan-Newman method for graph partitioning. In this chapter we present a novel approach for the computation of the betweenness centrality, which speeds up considerably Brandes’ algorithm (the current state of the art) in the context of social networks. Our approach exploits the natural sparsity of the data to algebraically (and efficiently) determine the betweenness of those nodes forming trees (tree-nodes) in the social network. Moreover, for the residual network, which is often of much smaller size, we modify directly the Brandes’ algorithm so that we can remove the nodes already processed and perform the computation of the shortest paths only for the residual nodes. We also give a fast sampling-based algorithm that computes an approximation of the betweenness centrality values of the residual network while returns the exact value for the tree-nodes. This algorithm improves in speed and precision over current state of the art approximation methods. Tests conducted on a sample of publicly available large networks from the Stanford repository show that, for the exact algorithm, speed improvements of a factor ranging between 2 and 5 are possible on several such graphs, when the sparsity, measured by the ratio of tree-nodes to the total number of nodes, is in a medium range (30–50 %). For some large networks from the Stanford repository and for a sample of social networks provided by Sistemi Territoriali with high sparsity (80 % and above) tests show that our algorithm, named SPVB (for Shortest Path Vertex Betweenness), consistently runs between one and two orders of magnitude faster than the current state of the art exact algorithm.

Strong structural control centrality of a complex network

Abstract: We introduce the definition of strong structural control centrality, which represents the dimension of strong structurally controllable subspace or the capability of a single node to control an entire directed and weighted network in a strongly structural manner. A purely algebraic algorithm to calculate strong structural control centrality is proposed. Then we explore the quality of the strong structural control centrality. The relation between strong structural control centrality and the layer index in a directed tree inspires us to research (1) some fast methods to achieve strong structural control centrality and (2) the size relationship of strong structural control centralities of nodes belonging to different supernodes.

Evolving networks : From topology to dynamics

Abstract: A multi-local-world model is introduced to describe the evolving networks that have a localization property such as the Internet. Based on this model, we show that the traffic load defined by “betweenness centrality” on the multi-local-world scale-free networks’ model also follows a power law form. In this kind of network, a few vertices have heavier loads and so play more important roles than the others in the network.