Title: Comparative Network Analysis

Speaker: Sumeet Agarwal

Abstract: Many real-world systems are naturally represented as networks, and a diverse range of measures have been developed to characterise their structure. However, studies of networks typically employ only small, partly arbitrarily selected subsets of these, and the lack of a comparison makes it unclear which structural diagnostics are redundant or complementary. We present a highly comparative study of networks and network features, analysing a wide variety of networks, derived both from empirical obser- vation and from mathematical models. We collate and examine a total of over four hundred network diagnostics or summary statistics thereof. We demonstrate how our approach can be used to organise and classify net- works, as well as to obtain insights into how network structure relates to functionally relevant characteristics in a variety of settings. These include finding fast estimators for the solution of hard graph problems, detecting structural features of metabolic networks that correlate with biological evolution, and constructing summary statistics that allow for efficient fitting of generative models to observed networks, via an Approximate Bayesian algorithm. Our methodology provides a general data-driven ap- proach to aid the study and understanding of networks.