Regensburg 2013 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 11: Statistics and Dynamics of/on Networks (joint session BP/DY/SOE)

DY 11.7: Talk

Tuesday, March 12, 2013, 11:15–11:30, H47

A Network Generation Process for Temporal Graphs — •Peter A. Kolski^1,2, Thomas Selhorst¹, Markus Abel², and Arkady Pikovsky² — ¹Friedrich-Loeffler-Institut, Wusterhausen, Germany — ²University of Potsdam, Germany

In this work we show a mechanism for creating Temporal Graphs inspired by real world trade transportation. In the last years complex networks have been in the focus of theoretical and applied research. Although networks like the power grid or water assets have continuos flow on the edges, trade networks are intrinsically discrete. We present a generic model for the generation and evolution of these Temporal Graphs: A continuous state is assigned to each node, described by a dynamical process. In our case we use an integrate-and-fire model. Once a threshold is exceeded, a node becomes "active" and, according to a cost function, selects another active node. This way an edge is temporarily established. Through these edges, nodes interact by resetting their states to zero. In addition, the cost function is modified in a way that the probability to reuse the edge is increased. We present first results on the analysis of this model by i) the degree distribution of the graph formed of the aggregated edges and ii) the degree distribution at a single time. In addition, we study the differences between a two-dimensional and a full graph. In particular we discuss details in the temporal evolution of the degree distribution, as one of the most important characteristics.