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...

In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from practical points of view. In this contribution we present a module-based method to efficiently break complex networks. The procedure first identifies the communities in which the network can be represented, then it deletes the nodes (edges) th...

This article introduces a theory of proximal nerve complexes and nerve spokes, restricted to the triangulation of finite regions in the Euclidean plane. A nerve complex is a collection of filled triangles with a common vertex, covering a finite region of the plane. Structures called k-spokes, k ≥ 1, are a natural extension of nerve complexes. A k-spoke is the union of a collection of filled tri...

CSCI 5352 Lecture 3 3 September 2013 Prof. Aaron Clauset 1 Which vertices are important? A common question when analyzing the structure of a network is which vertices are more or less important? This is not yet a well-defined question, and thus how we answer it depends greatly on what we mean by important. There are several general classes of answers. One is to define importance in terms of str...

We formally introduce in this paper two parameters graph theory, namely, clique centrality and global centrality. Let G be a finite, simple undirected of order n. A is nonempty subset W \(\subseteq\) V (G) such that the subgraph \(\langle\)W\(\rangle\)G induced by complete. The maximum size any containing vertex u \(\in\) called G. Normalizing sum centralities all vertices will lead us to G, wh...

Title of dissertation: Diffusion, Infection and Social (Information) Network Database Chanhyun Kang, Doctor of Philosophy, 2015 Dissertation directed by: Professor V.S. Subrahmanian Department of Computer Science Research to analyze diffusive phenomena over large rich datasets has received considerable attention in recent years. Moreover, with the appearance and proliferation of online social n...

Keywords characterize the topics discussed in a document. Extracting a small set of keywords from a single document is an important problem in text mining. We propose a hybrid structural and statistical approach to extract keywords. We represent the given document as an undirected graph, whose vertices are words in the document and the edges are labeled with a dissimilarity measure between two ...

This chapter first introduces some complex network models and then gives both local and global stability conditions for complete synchronization of complex dynamical networks. In addition, the concept of virtual control of pinned complex dynamical networks is introduced to illustrate the principle of pinning control. The main reason is explained for why significantly less local controllers are ...

We identify three different levels of correlation (pairwise relative ordering, network-wide ranking and prediction through linearity) that could be assessed between a computationally-light centrality metric and a computationally-heavy centrality metric for real-world networks. The Kendall's concordance-based correlation measure could be used to quantitatively assess how well we could consider t...

In this paper we consider the structure of dynamically evolving networks modelling information and activity moving across a large set of vertices. We adopt the communicability concept that generalizes that of centrality which is defined for static networks. We define the primary network structure within the whole as comprising of the most influential vertices (both as senders and receivers of d...