Learning Mesh and Multiple Conserved Networks From Data

Reconstruction of network topology from data is one of the important problem in network science. Earlier, it has been shown that conserved tree-type (or radial) networks can be reconstructed from flow data exactly by combining learning method with graph realization problem [1]. However, the current approach in [1] allows to reconstruct meshed (looped) networks up to 2-isomorphism. Then, the following question arises for reconstruction of meshed networks (Q1) “Is it possible to exactly reconstruct meshed networks? If the answer to Question Q1 is positive, then, the next question is: (Q2) What information do we need to specify to exactly reconstruct these networks? Further, in [1], it is assumed that measured data are collected from one underlying network. However, measured data are collected from several networks. Then, the question is: (Q3) “How do we reconstruct several networks from measured data? In this proposal, we will investigate these three questions.