No-exclaves percolation.

Network robustness has been a pivotal issue in the study of system failure in network science since its inception. To shed light on this subject, we introduce and study a new percolation process based on a new cluster called an 'exclave' cluster. The entities comprising exclave clusters in a network are the sets of connected unfailed nodes that are completely surrounded by the failed (i.e., nonfunctional) nodes. The exclave clusters are thus detached from other unfailed parts of the network, thereby becoming effectively nonfunctional. This process defines a new class of clusters of nonfunctional nodes. We call it the no-exclave percolation cluster (NExP cluster), formed by the connected union of failed clusters and the exclave clusters they enclose. Here we showcase the effect of NExP cluster, suggesting a wide and disruptive collapse in two empirical infrastructure networks. We also study on two-dimensional Euclidean lattice to analyze the phase transition behavior using finite-size scaling. The NExP model considering the collective failure clusters uncovers new aspects of network collapse as a percolation process, such as quantitative change of transition point and qualitative change of transition type. Our study discloses hidden indirect damage added to the damage directly from attacks, and thus suggests a new useful way for finding nonfunctioning areas in complex systems under external perturbations as well as internal partial closures.

Layer-switching cost and optimality in information spreading on multiplex networks.

We study a model of information spreading on multiplex networks, in which agents interact through multiple interaction channels (layers), say online vs. offline communication layers, subject to layer-switching cost for transmissions across different interaction layers. The model is characterized by the layer-wise path-dependent transmissibility over a contact, that is dynamically determined dependently on both incoming and outgoing transmission layers. We formulate an analytical framework to deal with such path-dependent transmissibility and demonstrate the nontrivial interplay between the multiplexity and spreading dynamics, including optimality. It is shown that the epidemic threshold and prevalence respond to the layer-switching cost non-monotonically and that the optimal conditions can change in abrupt non-analytic ways, depending also on the densities of network layers and the type of seed infections. Our results elucidate the essential role of multiplexity that its explicit consideration should be crucial for realistic modeling and prediction of spreading phenomena on multiplex social networks in an era of ever-diversifying social interaction layers.