Topological identification in networks of dynamical systems

TL;DR

This paper introduces a method for reconstructing the topology of networks of dynamical systems using a distance function, with theoretical guarantees for linear systems with tree topology and an application to stock market data.

Contribution

It proposes a novel distance-based approach for topological identification in dynamical networks, including theoretical validation and real-world application.

Findings

The method accurately reconstructs network topology for linear systems with tree structure.

The approach is validated on high-frequency stock market data.

Theoretical guarantees ensure the correctness of the identification process.

Abstract

The paper deals with the problem of reconstructing the topological structure of a network of dynamical systems. A distance function is defined in order to evaluate the "closeness" of two processes and a few useful mathematical properties are derived. Theoretical results to guarantee the correctness of the identification procedure for networked linear systems with tree topology are provided as well. Finally, the application of the techniques to the analysis of an actual complex network, i.e. to high frequency time series of the stock market, is illustrated.