Maximum likelihood estimation for social network dynamics

A model for network panel data is discussed, based on the assumption that the observed data are discrete observations of a continuous-time Markov process on the space of all directed graphs on a given node set, in which changes in tie variables are independent conditional on the current graph. The model for tie changes is parametric and designed for applications to social network analysis, where the network dynamics can be interpreted as being generated by choices made by the social actors represented by the nodes of the graph. An algorithm for calculating the Maximum Likelihood estimator is presented, based on data augmentation and stochastic approximation. An application to an evolving friendship network is given and a small simulation study is presented which suggests that for small data sets the Maximum Likelihood estimator is more efficient than the earlier proposed Method of Moments estimator.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS313 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Socially Structured Games and their Applications

In this paper we generalize the concept of a non-transferable utility game by introducing the concept of a socially structured game.A socially structured game is given by a set of players, a possibly empty collection of internal organizations on any subset of players, for any internal organization a set of attainable payo.s and a function on the collection of all internal organizations measuring the power of every player within the internal organization.Any socially structured game induces a non-transferable utility game.In the derived nontransferable utility game, all information concerning the dependence of attainable payo.s on the internal organization gets lost.We show this information to be useful for studying non-emptiness and re.nements of the core. For a socially structured game we generalize the concept of p-balancedness to social stability and show that a socially stable game has a non-empty socially stable core.In order to derive this result, we formulate a new intersection theorem that generalizes the KKM-Shapley intersection theorem.The socially stable core is a subset of the core of the game.We give an example of a socially structured game that satis.es social stability, whose induced non-transferable utility game therefore has a non-empty core, but does not satisfy p-balanced for any choice of p.The usefulness of the new concept is illustrated by some applications and examples.In particular we de.ne a socially structured game, whose unique element of the socially stable core corresponds to the Cournot-Nash equilibrium of a Cournot duopoly.This places the paper in the Nash research program, looking for a unifying approach to cooperative and non-cooperative behavior in which each theory helps to justify and clarify the other.game theory

Animating the development of Social Networks over time using a dynamic extension of multidimensional scaling

The animation of network visualizations poses technical and theoretical challenges. Rather stable patterns are required before the mental map enables a user to make inferences over time. In order to enhance stability, we developed an extension of stress-minimization with developments over time. This dynamic layouter is no longer based on linear interpolation between independent static visualizations, but change over time is used as a parameter in the optimization. Because of our focus on structural change versus stability the attention is shifted from the relational graph to the latent eigenvectors of matrices. The approach is illustrated with animations for the journal citation environments of Social Networks, the (co-)author networks in the carrying community of this journal, and the topical development using relations among its title words. Our results are also compared with animations based on PajekToSVGAnim and SoNIA

Social Network Analysis with sna

Modern social network analysis---the analysis of relational data arising from social systems---is a computationally intensive area of research. Here, we provide an overview of a software package which provides support for a range of network analytic functionality within the R statistical computing environment. General categories of currently supported functionality are described, and brief examples of package syntax and usage are shown.

Genetic Representations for Evolutionary Minimization of Network Coding Resources

We demonstrate how a genetic algorithm solves the problem of minimizing the resources used for network coding, subject to a throughput constraint, in a multicast scenario. A genetic algorithm avoids the computational complexity that makes the problem NP-hard and, for our experiments, greatly improves on sub-optimal solutions of established methods. We compare two different genotype encodings, which tradeoff search space size with fitness landscape, as well as the associated genetic operators. Our finding favors a smaller encoding despite its fewer intermediate solutions and demonstrates the impact of the modularity enforced by genetic operators on the performance of the algorithm.Comment: 10 pages, 3 figures, accepted to the 4th European Workshop on the Application of Nature-Inspired Techniques to Telecommunication Networks and Other Connected Systems (EvoCOMNET 2007

A graph interpretation of the least squares ranking method

The paper aims at analyzing the least squares ranking method for generalized tournaments with possible missing and multiple paired comparisons. The bilateral relationships may reflect the out- comes of a sport competition, product comparisons, or evaluation of political candidates and policies. It is shown that the rating vector can be obtained as a limit point of an iterative process based on the scores in almost all cases. The calculation is interpreted on an undirected graph with loops attached to some nodes, revealing that the procedure takes into account not only the given object’s results but also the strength of objects compared with it. We explore the connection between this method and another procedure defined for ranking the nodes in a digraph, the positional power measure. The decomposition of the least squares solution offers a number of ways to modify the method