Networks constitute a paradigm of complexity in real life systems by assembling the structure of the interactions of their elementary constituents [2, 3]. They are found at every level of biological organisation, from genes inside the cells to the trophic relations between species in large ecosys- tems [3]. Nowadays, with the enormous development of data science, there is a huge interest re- lated to the network inference, namely detecting the interacting structure from external measure- ments or observations. For example, reconstructing the structure of brain networks from the activi- ty of neuronal patches has been a major goal in computational neuroscience. The dynamics that takes place on networked systems can, in some cases, strongly influence the perception that we have regarding local topological features such as the degree [4] or global ones such as network non-normality [5]. In this work, we focus specifically on the problem of measuring network cen- tralities from the dynamical point of view. We show that the inference of networks’ structural properties depends heavily on the competition between the node-based dynamics on one hand and the interactions between the nodes on the other. In particular, we illustrate such a phenomenon based on the communicability centrality, considered as a reliable measure for dynamical inference. We show that when the local intra-nodes dynamics is slower than the inter-nodes one then the ranking of the nodes according to the standard definition of the communicability, becomes inade- quate. Such ranking can be enhanced if further information regarding the nature of the dynamics occurring on the network is available. As an example, we show that for networks with different time-scale structures such as strong modularity, the existence of fast global dynamics can imply that precise inference of the community structure is impossible (see Fig. 1).
[1] M. Asllani, T. Carletti, F. Di Patti, D. Fanelli, F. Piazza, Phys. Rev. Lett. 120(15) 158301 (2020).
[2] E. Estrada, The structure of complex networks: theory and applications, Oxford University Press (2012).
[3] M. E. J. Newman, Networks: An Introduction, Oxford University Press (2010)
[4] M. Asllani, T. Carletti, F. Di Patti, D. Fanelli, F. Piazza, Phys. Rev. Lett. 120(15) 158301 (2018).
[5] M. Asllani, R. Lambiotte and T. Carletti, Sci. Adv. 4 eaau 9403 (2018).