Institute for Theoretical Physics - University of Würzburg
Analyses of economic networks using the toolbox of statistical physics
Over the last ten years, advances in information technology have allowed to record and make available an avalanche of relational data, aka networks, that describe the interactions of thousands of human agents in various contexts. These span from communications in large scale telephone connection data, email exchange, internet dating or social networking sites to various markets, both online and offline, such as the eBay auction platform or the UN commodity trade database. These data sets allow for quantitative studies of unprecedented detail and scope. At the same time, a number of new data analysis methods has been developed that allow to gain insight into the structure of these data, some of which are inspired by methods from statistical physics. In my talk, I will present a framework for the detection of functional roles based on connectivity patterns in (market-)networks. The formalism merges the sociological concepts of structural and regular equivalence into a density based generalization of block modeling. Using a first principles approach, I derive a measure for the fit of a network to any given block model allowing objective hypothesis testing. From the generic properties of an optimal fit, I derive how to find the best fitting block model directly from the data and present a criterion to avoid over-fitting. The method can handle both two-mode and one-mode data, directed and undirected networks as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is non-parametric and computationally efficient. Example applications to market research problems are given which show the accuracy and predictive power of this approach. Finally, I will show how methods from statistical physics can be used to calculate the detection accuracy and establish universal bounds on what kinds of patterns can be detected independent of the algorithm used.