Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes in a network, a classical metric is centrality within which there are multiple specific instances including degree centrality, closeness centrality, betweenn...

Estimating the relative importance of vertices and edges is a fundamental issue in the analysis of complex networks, and has found vast applications in various aspects, such as social networks, power grids, and biological networks. Most previous work focuses on metrics of vertex importance and methods for identifying powerful vertices, while related work for edges is much lesser, especially for...

In a recent work we introduced a measure of importance for groups of vertices in a complex network. This centrality for groups is always between 0 and 1 and induces the eigenvector centrality over vertices. Furthermore, its value over any group is the fraction of all network flows intercepted by this group. Here we provide the rigorous mathematical constructions underpinning these results via a...

Processing large graphs is an emerging and increasingly important computation in a variety of application domains, from social networking to genomics and marketing. One of the important and computationally challenging structural graph metrics is node betweenness centrality, a measure of influence of a node in the graph. The best known algorithm for computing exact betweenness centrality runs in...

Functional magnetic resonance data acquired in a task-absent condition ("resting state") require new data analysis techniques that do not depend on an activation model. In this work, we introduce an alternative assumption- and parameter-free method based on a particular form of node centrality called eigenvector centrality. Eigenvector centrality attributes a value to each voxel in the brain su...

Centrality has revealed crucial for understanding the structural properties of complex relational networks. Centrality is also relevant for various spatial factors affecting human life and behaviors in cities. Here, we present a comprehensive study of centrality distributions over geographic networks of urban streets. Five different measures of centrality, namely degree, closeness, betweenness,...

Ernesto Estrada Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK The discriminant power of centrality indices for the degree, eigenvector, closeness, betweenness and subgraph centrality is analyzed. It is defined by the number of graphs for which the standard deviation of the centrality of its nodes is zero. On the basis of empirical analysis it is conclud...

This study describes an outlier detection technique for graph structure data that uses the centrality index. Existing techniques set thresholds for link and node regularity. However, existing techniques are not objective and do not apply to data without the link strength information. Therefore, we pay attention to centrality, which is an index used in network analysis. We perform outlier detect...

The study is based on the re-combination or synthesis of international scientific literature, and definition notions center , sub-center . A conceptual-structural framework socio-spatial characteristics centers (and sub-centers) set up, these factors are essential elements making, maintaining, rehabilitating a city: Market Competition; Node Pole; Faith; Power; Security; Mixture; Identity In an ...