Inverse problem of networks-reconstruction of graph

Authors:
Lei Wang;Gen Qi Xu;Nikos E. Mastorakis
Affiliations:
Tianjin University, Department of Mathematics, Tianjin, China;Tianjin University, Department of Mathematics, Tianjin, China;Military Institutes of University Education, Hellenic Naval Academy, Piraeus, Greece
Venue:
ISTASC'10 Proceedings of the 10th WSEAS international conference on Systems theory and scientific computation
Year:
2010

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Abstract

In this note, we report a new approach in reconstruction of the general complex network based on the system test. Suppose that there is a 1-d wave system defined on a metric graph, and the state of system is measurable. Firstly, we determine the Green function matrix of any given complex network by the Laplace transform of the state. Secondly, we obtain the relationship between the Green function matrix and the incident matrix, from which we reconstruct the complex network for any given Green function matrix.