Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

An adjacency criterion for the prime graph of a finite simple group

Abstract: In the paper we give an exhaustive arithmetic criterion of adjacency in prime graph $GK(G)$ for every finite nonabelian simple group $G$. By using this criterion for all finite simple groups an independence set with the maximal number of vertices, an independence set containing 2 with the maximal number of vertices, and the orders of these independence sets are given. We assemble this information in the tables at the end of the paper. Several applications of obtained results for various problems of finite group theory are considered.

Minimal representation of directed hypergraphs

Abstract: In this paper the problem of minimal representations for particular classes of directed hypergraphs is analyzed. Various concepts of minimal representations of directed hypergraphs (called minimal equivalent hypergraphs) are introduced as extensions to the concepts of transitive reduction and minimum equivalent graph of directed graphs. In particular, we consider equivalent hypergraphs which are minimal with respect to all parameters which may be adopted to characterize a given hypergraph (number of hyperarcs, number of adjacency lists required for the representation, length of the overall description,etc.). The relationships among the various concepts of minimality are discussed and their computational properties are analyzed. In order to derive such results, a graph representation of hypergraphs is introduced.

Graph Theoretic and Spectral Analysis of Enron Email Data

Abstract: Analysis of social networks to identify communities and model their evolution has been an active area of recent research. This paper analyzes the Enron email data set to discover structures within the organization. The analysis is based on constructing an email graph and studying its properties with both graph theoretical and spectral analysis techniques. The graph theoretical analysis includes the computation of several graph metrics such as degree distribution, average distance ratio, clustering coefficient and compactness over the email graph. The spectral analysis shows that the email adjacency matrix has a rank-2 approximation. It is shown that preprocessing of data has significant impact on the results, thus a standard form is needed for establishing a benchmark data.

Multiple coordinated views for network attack graphs

Abstract: While efficient graph-based representations have been developed for modeling combinations of low-level network attacks, relatively little attention has been paid to effective techniques for visualizing such attack graphs. This paper describes a number of new attack graph visualization techniques, each having certain desirable properties and offering different perspectives for solving different kinds of problems. Moreover, the techniques we describe can be applied not only separately, but can also be combined into coordinated attack graph views. We apply improved visual clustering to previously described network protection domains (attack graph cliques), which reduces graph complexity and makes the overall attack flow easier to understand. We also visualize the attack graph adjacency matrix, which shows patterns of network attack while avoiding the clutter usually associated with drawing large graphs. We show how the attack graph adjacency matrix concisely conveys the impact of network configuration changes on attack graphs. We also describe a novel attack graph filtering technique based on the interactive navigation of a hierarchy of attack graph constraints. Overall, our techniques scale quadratically with the number of machines in the attack graph.

Boundary Detection in Multidimensions

Abstract: The development of image processing algorithms for time-varying imagery and computerized tomography data calls for generalization of the concepts of adjacency, connectivity, boundary, etc., to three and four-dimensional discrete spaces. This paper defines these basic concepts in unified terminology and presents algorithms for a boundary detection task in multidimensional space. The performance of these algorithms is discussed with respect to theoretical maximum complexity, and is illustrated with simulated computerized tomography data.