Exploring trapping problem on simplicial networks encoding higher-order interactions

Abstract

Biological, social and man-made systems often harbor various types of higher-order interaction, whose presence may substantially impact the dynamics on these systems. As a special random walk, paradigmatic trapping problem is still scarcely explored on networks encoding higher-order interactions. In this paper, applying simplicial networks produced by edge corona product as test bed, we explore how the higher-order interaction impact trapping process. Specifically, an immobile trap is first deployed at an initial node of the networks and average trapping time (ATT) is derived analytically to measure trapping efficiency of standard weight-dependent random walk. Then, delayed random walk incorporating delay phenomenon into random walk process is introduced into the networks and closed form solution of ATT is still obtained for quantifying trapping efficiency. The obtained analytical solutions of ATT in both scenarios show that ATT grows sub-linearly with network size but its leading scaling is quantitatively dependent on the parameter specifying building block of networks. Besides, analytical expression of ATT obtained in the latter scenario shows that the parameter [Formula: see text] manipulating delayed random walk does not affect the leading scaling of ATT but can quantitatively modify its prefactor. Therefore, introduction of delay phenomenon still can modulate trapping efficiency quantitatively in the presence of higher-order interaction. This work may pave the way for modulating trapping process and related dynamical processes on general networks modeling higher-order interactions.