Regular Article

Reactive explorers to unravel network topology

¹ Dipartimento di Ingegneria dell’Informazione, Università di Firenze, Via S. Marta 3, 50139 Florence, Italy
² Università degli Studi di Firenze, Dipartimento di Fisica e Astronomia, CSDC and INFN, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
³ Dipartimento di Fisica e Astronomia and CSDC, Università degli Studi di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
⁴ INFN Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
⁵ naXys, Namur Institute for Complex Systems, University of Namur, Namur, Belgium

^a e-mail: duccio.fanelli@unifi.it

Received: 29 November 2018
Received in final form: 21 March 2019
Published online: 8 May 2019

Abstract

A procedure is developed and tested to recover the distribution of connectivity of an a priori unknown network, by sampling the dynamics of an ensemble made of reactive walkers. The relative weight between reaction and relocation is gauged by a scalar control parameter, which can be adjusted at will. Different equilibria are attained by the system, following the externally imposed modulation, and reflecting the interplay between reaction and diffusion terms. The information gathered on the observation node is used to predict the stationary density as displayed by the system, via a direct implementation of the celebrated Heterogeneous Mean Field (HMF) approximation. This knowledge translates into a linear problem which can be solved to return the entries of the sought distribution. A variant of the model is then considered which consists in assuming a localized source where the reactive constituents are injected, at a rate that can be adjusted as a stepwise function of time. The linear problem obtained when operating in this setting allows one to recover a fair estimate of the underlying system size. Numerical experiments are carried so as to challenge the predictive ability of the theory.