|
Abstract:
|
There is a trend to analyze large collections of networks, e.g., collections of ego-centric subnetworks on Facebook. In recent work by our group, a formal notion of a space of network Graph Laplacians has been introduced and a central limit theorem has been developed based on it. Hypothesis testing is then implemented. However, in many natural and engineered systems multilayer networks arise naturally, e.g., in computational biology and neuroscience . In this project, we considered two useful classes of multilayer network, differing from each other in the form of their inter-layer connection. Defining a corresponding space of supra-Laplacians for these networks, we established the necessary geometry of this space and a central limit theorem. These results then enabled us to develop tests of various classes of hypotheses relevant to multilayer networks. Simulations and real data examples were used to illustrate performance of our approach.
|
