“…Network reconstruction problems, in which one aims at reconstructing a network structure from the observation of a signal evolving on it, is an important topic of current research, spanning over numerous domains (Marc Timme and Casadiego 2014; Shandilya and Marc Timme 2011; Dong et al 2015; Le Bars et al 2019; Sardellitti, Barbarossa, and Lorenzo 2019). Indeed, the widespread use of networks as a modelling tool in fields as diverse as telecommunications (Pastor-Satorras and Vespignani 2004; Newman, Watts, and Strogatz 2002), genetics (Gardner et al 2003; Karlebach and Shamir 2008), ecology (Hanski and Gilpin 1997; Tamburello, O. Ma, and M. Côté 2019), or transportation of goods or humans (Youn, Gastner, and Jeong 2008;Perfido et al 2017), to name but a few, makes understanding the connections between their structure, or internal properties, and the phenomena which happen over them, a crucial issue.…”