Article,
The effect of spatiality on multiplex networks
EPL (Europhysics Letters), 115 (3): 36002+ (Aug 1, 2016)
DOI: 10.1209/0295-5075/115/36002
Abstract
Multilayer infrastructure is often interdependent, with nodes in one layer
depending on nearby nodes in another layer to function. The links in each layer
are often of limited length, due to the construction cost of longer links.
Here, we model such systems as a multiplex network composed of two or more
layers, each with links of characteristic geographic length, embedded in
2-dimensional space. This is equivalent to a system of interdependent spatially
embedded networks in two dimensions in which the connectivity links are
constrained in length but varied while the length of the dependency links is
always zero. We find two distinct percolation transition behaviors depending on
the characteristic length, \$\zeta\$, of the links. When \$\zeta\$ is longer than a
certain critical value, \$\zeta\_c\$, abrupt, first-order transitions take place,
while for \$\zeta<\zeta\_c\$ the transition is continuous. We show that, though in
single-layer networks increasing \$\zeta\$ decreases the percolation threshold
\$p\_c\$, in multiplex networks it has the opposite effect: increasing \$p\_c\$ to a
maximum at \$\zeta=\zeta\_c\$. By providing a more realistic topological model for
spatially embedded interdependent and multiplex networks and highlighting its
similarities to lattice-based models, we provide a new direction for more
detailed future studies.
