We investigate the correlation between the information theoretic measure of empowerment and the graph theoretic measure of closeness centrality, to better understand the structural conditions that must exist in a world for learning and adaptation. We examine both measures in both a simple gridworld scenario, represented as a graph, and on a scale-free graph. We show a strong correlation between the two measures, and discuss the strengths and weaknesses of both. We go on to show how the local measurement of empowerment can in many cases predict a measure for the global measurement of closeness centrality.

Freeman’s (1979) measure of closeness centrality is valuable in network analysis, but its use is limited to connected networks. In this paper, I describe an approach for calculating actor closeness centrality that circumvents the problem of disconnectedness. I show how the complement, G C, of a disconnected network, G, can be used to obtain weights that transform Freeman’s measure, C ' C, into a universal measure, C ' CW, for actors in both connected and disconnected networks. In essence, this method incorporates information about how an actor is not proximate to all other actors in a network (captured by the structure of the complement network) to weight within-component closeness. C ' CW has several attractive properties. Aside from being universally applicable and ranging from 0 to 1, the value of C ' CW equals C ' C in connected networks. Furthermore, C ' CW cannot reach 1 for actors in disconnected networks.

Graduate School This paper presents a new way to monitor and look at adversarial networks through the Adversarial Network Analyzer (ANA) and supporting mathematical calculations. Recent work on social networks has begun to be used in the analysis of adversarial networks and their underlying structure with hopes of detecting and preventing future activity. Adversarial networks are abstracted to be network subgroups that work against the interests of the group studying it. ANA, the software package created by this work, can be a tool for network visualization and a teaching exercise for students in the field of security analysis. It can portray the structure of such networks and allow analysts to find patterns and key players in the network while watching the network evolve to carry out a goal. Finally, this thesis uses output from ANA to study how a simulated adversarial scenario grows in structure. I compare this network against more traditional social networks on standard measures and also analyze the change in time of this network on those same

network visualization, social network, simulation, adversarial networks, development of networks ABSTRACT: We present a novel way to monitor and analyze the time course of adversarial networks through a simulation tool and supporting mathematical analysis. Recent work on social networks has been used in the analysis of adversarial networks and their underlying structure with hopes of detecting and preventing future activity. In this paper we consider an adversarial network to be a network subgroup that works against the interests of the group studying it. ANA, the software package presented here, can portray the structure of such networks and allow analysts to find patterns and key players in the network while watching the network evolve. Finally, this work uses output from ANA to study how a simulated adversarial scenario grows in structure and compares it to more traditional social networks on standard measures and also analyze the changes over time of this network on those same dimensions. 1.

A lot of centrality measures have been developed to analyze different aspects of importance. Some of the most popular centrality measures (e.g. betweenness centrality, closeness centrality) are based on the calculation of shortest paths. This characteristic limits the applicability of these measures for larger networks. In this article we elaborate on the idea of boundeddistance shortest paths calculations. We claim criteria for k-centrality measures and we introduce one algorithm for calculating both betweenness and closeness based centralities. We also present normalizations for these measures. We show that k-centrality measures are good approximations for the corresponding centrality measures by achieving a tremendous gain of calculation time and also having linear calculation complexity Θ(n) for networks with constant average degree. This allows researchers to approximate centrality measures based on shortest paths for networks with millions of nodes or with high frequency in dynamically changing networks.