title: Temporal correlation coefficient for directed networks.
abstract: Previous studies dealing with network theory focused mainly on the static aggregation of edges over specific time window lengths. Thus, most of the dynamic information gets lost. To assess the quality of such a static aggregation the temporal correlation coefficient can be calculated. It measures the overall possibility for an edge to persist between two consecutive snapshots. Up to now, this measure is only defined for undirected networks. Therefore, we introduce the adaption of the temporal correlation coefficient to directed networks. This new methodology enables the distinction between ingoing and outgoing edges. Besides a small example network presenting the single calculation steps, we also calculated the proposed measurements for a real pig trade network to emphasize the importance of considering the edge direction. The farm types at the beginning of the pork supply chain showed clearly higher values for the outgoing temporal correlation coefficient compared to the farm types at the end of the pork supply chain. These farm types showed higher values for the ingoing temporal correlation coefficient. The temporal correlation coefficient is a valuable tool to understand the structural dynamics of these systems, as it assesses the consistency of the edge configuration. The adaption of this measure for directed networks may help to preserve meaningful additional information about the investigated network that might get lost if the edge directions are ignored.
authors: Institute of Animal Breeding and Husbandry, Christian-Albrechts-University, Olshausenstr. 40, 24098 Kiel, Germany.
authors: Kathrin
authors: K
authors: Büttner
authors: Institute of Animal Breeding and Husbandry, Christian-Albrechts-University, Olshausenstr. 40, 24098 Kiel, Germany.
authors: Jennifer
authors: J
authors: Salau
authors: Institute of Animal Breeding and Husbandry, Christian-Albrechts-University, Olshausenstr. 40, 24098 Kiel, Germany.
authors: Joachim
authors: J
authors: Krieter
keywords: Directed network; Temporal correlation coefficient; Temporal network; Topological overlap