Information theory in complex networks
– Online Colloquium
Martin Roswall (University of Umeå, Sweden) und Karoline Wiesner (University of Potsdam, Germany)
2 pm Martin Roswall (University of Umeå): Mapping network flows with incomplete information
3:15 pm Karoline Wiesner (University of Potsdam): Information entropy in complex systems: Mathematical foundations and their meaning
Martin Roswall (University of Umeå):Mapping network flows with incomplete information
Abstract: After a gentle introduction to the information-theoretic and flow-based community detection method known as Infomap, I will present recent work on analyzing networks with missing data. Detecting significant community structure in networks with incomplete observations is challenging because the evidence for specific solutions fades away with missing data. I will explain how we have addressed this problem with the Bayesian estimate of the map equation for unweighted and undirected networks and extended the idea to enable more robust community detection in weighted and directed networks. I will show how an efficient implementation in Infomap provides more reliable communities even with a significant fraction of the data missing.
Karoline Wiesner (University of Potsdam): Information entropy in complex systems: Mathematical foundations and their meaning
Abstract: We begin with an introduction to the nature of complex systems, followed by a brief discussion of the role of information theory in the analysis of complex systems. In particular, we distinguish between information processing -- in the sense of encoding and transmitting a symbolic representation — and the formation of correlations (pattern formation / self-organisation). Continuing with the latter, we then introduce the paired cumulative entropy, an entropy for cumulative probability densities and interpret it as a measure of heterogeneity. Its application to complex networks and network robustness will illustrate the fruitful connection between information theory and complex systems.
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