k-core requires something more
The organization of a network in tightly knitted groups of nodes with at least k connections known as k-shell (k-cores) structure/decomposition has been used to study several phenomena associated with, e.g., spreading dynamics. It has been proven, in fact, that nodes in the innermost k-shells play a crucial role in the diffusion of pathogens, emergence of consensus, and resilience of the system. The k-shell decomposition of several empirical networks displays non-trivial features. It is therefore legitimate to ask whether such features are amenable to the degree sequence of the nodes or if, instead, a generative model needs to account also for other ‘ingredients’. In this talk, I will present the results of a study aimed at testing such hypothesis. Given some empirical and synthetic networks, I will study their k-shell decomposition as well as that of some suitably ‘randomized’ counterparts, and then show how the k-core structure needs something more than the degree in order to be reproduced.