title: Networks: On the relation of bi- and multivariate measures.
abstract: A reliable inference of networks from observations of the nodes' dynamics is a major challenge in physics. Interdependence measures such as a the correlation coefficient or more advanced methods based on, e.g., analytic phases of signals are employed. For several of these interdependence measures, multivariate counterparts exist that promise to enable distinguishing direct and indirect connections. Here, we demonstrate analytically how bivariate measures relate to the respective multivariate ones; this knowledge will in turn be used to demonstrate the implications of thresholded bivariate measures for network inference. Particularly, we show, that random networks are falsely identified as small-world networks if observations thereof are treated by bivariate methods. We will employ the correlation coefficient as an example for such an interdependence measure. The results can be readily transferred to all interdependence measures partializing for information of thirds in their multivariate counterparts.
authors.affiliation: 1] Institute of Physics, University of Freiburg, Germany [2] Freiburg Center of Data Analysis and Modeling, University of Freiburg, Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Mader
authors.affiliation: 1] Institute of Physics, University of Freiburg, Germany [2] Freiburg Center of Data Analysis and Modeling, University of Freiburg, Germany [3] University Medical Center Freiburg, Germany.
authors.forename: Malenka
authors.initials: M
authors.lastname: Mader
authors.affiliation: 1] Institute of Physics, University of Freiburg, Germany [2] Freiburg Center of Data Analysis and Modeling, University of Freiburg, Germany [3] BIOSS, Center for Biological Signalling Studies, University of Freiburg, Germany.
authors.forename: Jens
authors.initials: J
authors.lastname: Timmer
authors.affiliation: University of Aberdeen, UK.
authors.forename: Marco
authors.initials: M
authors.lastname: Thiel
authors.affiliation: 1] Institute of Physics, University of Freiburg, Germany [2] University of Aberdeen, UK.
authors.forename: Björn
authors.initials: B
authors.lastname: Schelter