The effect of spatiality on multiplex networks (Vol. 47 No. 5-6)

When a node can only form a link to its nearest neighbour, the topology is entirely determined by the spatial locations of the nodes. But when near and far links can form, the influence of the spatial embedding of the topology is much less. In this paper, we use this to modulate the strength of spatial effects on network topology. This allows us to consider the question: Does increasing the allowed geometric length of links in a network improve its robustness? In single-layer networks, the answer is generally that it does. However, in multiplex networks, we find that increasing the link lengths actually makes the network vulnerable to more severe cascade behaviours. This is because in multiplex networks, longer links allow for a discontinuous percolation transition which is characterized by a nucleation process. Our model and results demonstrate the surprising effects of spatial embedding and provide a simple new framework for assessing spatial networks of one or more layers.

M. M. Danziger, L. M. Shekhtman, Y. Berezin and S. Havlin, The effect of spatiality on multiplex networks, EPL 115, 36002 (2016)
[Abstract]