A new measure of centrality, C,, is introduced. It is based on the concept of network flows. While conceptually similar to Freeman’s original measure, Ca, the new measure differs from the original in two important ways. First, C, is defined for both valued and non-valued graphs. This makes C, applicable to a wider variety of network datasets. Second, the computation of C, is not based on geodesic paths as is C, but on all the independent paths between all pairs of points in the network.

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The dynamics of social networks are modeled with a system of continuous Stochastic Ordinary Differential Equations (SODE). With the proper amount of noise input, the SODE model captures dynamic features that are lacking in the corresponding deterministic ODE model. Therefore, sensitivity to noise levels is investigated by considering four different regimes: essentially deterministic, noise-enriched, noise-enlarged, and noise-dominated. Each regime is defined based on the behavior of solutions of the SODE and geometry of the regimes are categorized with stochastic simulations.

Social Network Analysis is a widely used approach in psychology, as in social science, economics and other fields. The peculiarity of this perspective is that it focuses not on individuals or other social units, but on the relationship between them. In this paper, our aim is to give a general review of this perspective, giving a description of resources and principal topics covered by Social Network Analysis. In the first section, we will concentrate on methodological and formal perspectives of analysis. In the last section, we will introduce some recent studies about Social Network and its relationship with Information Technologies, in particular on the Internet. Lastly, we will show how this approach can be useful to study some aspects of the web.

This note tries to attempt a sketch of the history of spectral ranking—a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather some kind of relationship between entities. Albeit recently made famous by the ample press coverage of Google’s PageRank algorithm, spectral ranking was devised more than fifty years ago, almost exactly in the same terms, and has been studied in psychology and social sciences. I will try to describe it in precise and modern mathematical terms, highlighting along the way the contributions given by previous scholars. Disclaimer This is is a work in progress with no claim of completeness. I have tried to collect evidence of spectral techniques in ranking from a number of sources, providing a unified mathematical framework that should make it possible to understand in a precise way the relationship between contributions. Reports of inaccuracies and missing references are more than welcome. 1

DMS-0112069. Any opinions, findings, and conclusions or recommendations expressed in this material are

The mathematical definition of clique has never been entirely satisfactory when it comes to providing a procedure for defining human social groups. This paper shows how the Galois structure of containment among cliques and actors can be used to produce an intuitively appealing characterization of groups--one that is consistent with ethnographic descriptions. Two examples, using 'classical ' social network data sets, are provided. 1.