Dominating sets and ego-centered decompositions in social networks

Our aim here is to address the problem of decomposing a whole network into a minimal number of ego-centered subnetworks. For this purpose, the network egos are picked out as the members of a minimum dominating set of the network. However, to find such an efficient dominating ego-centered construction, we need to be able to detect all the minimum dominating sets and to compare all the corresponding dominating ego-centered decompositions of the network. To find all the minimum dominating sets of the network, we are developing a computational heuristic, which is based on the partition of the set of nodes of a graph into three subsets, the always dominant vertices, the possible dominant vertices and the never dominant vertices, when the domination number of the network is known. To compare the ensuing dominating ego-centered decompositions of the network, we are introducing a number of structural measures that count the number of nodes and links inside and across the ego-centered subnetworks. Furthermore, we are applying the techniques of graph domination and ego=centered decomposition for six empirical social networks.Comment: 17 pages, 7 figure

Analysis of Layered Social Networks

Prevention of near-term terrorist attacks requires an understanding of current terrorist organizations to include their composition, the actors involved, and how they operate to achieve their objectives. To aid this understanding, operations research, sociological, and behavioral theory relevant to the study of social networks are applied, thereby providing theoretical foundations for new methodologies to analyze non-cooperative organizations, defined as those trying to hide their structure or are unwilling to provide information regarding their operations. Techniques applying information regarding multiple dimensions of interpersonal relationships, inferring from them the strengths of interpersonal ties, are explored. A layered network construct is offered that provides new analytic opportunities and insights generally unaccounted for in traditional social network analyses. These provide decision makers improved courses of action designed to impute influence upon an adversarial network, thereby achieving a desired influence, perception, or outcome to one or more actors within the target network. This knowledge may also be used to identify key individuals, relationships, and organizational practices. Subsequently, such analysis may lead to the identification of exploitable weaknesses to either eliminate the network as a whole, cause it to become operationally ineffective, or influence it to directly or indirectly support National Security Strategy