Line graphs for a multiplex network

On the edges' PageRank and line graphs

Two different approaches on a directed (and possibly weighted) network G are considered in order to define the PageRank of each edge of G with the focus on its applications. It is shown that both approaches are equivalent, even though it is clear that one approach has clear computational advantages over the other. The usefulness of this concept in the context of applications is illustrated by means of some examples within the area of cybersecurity and some simulations and examples within the scope of subway networks.

Multiplex multivariate recurrence network from multi-channel signals for revealing oil-water spatial flow behavior

The exploration of the spatial dynamical flow behaviors of oil-water flows has attracted increasing interests on account of its challenging complexity and great significance. We first technically design a double-layer distributed-sector conductance sensor and systematically carry out oil-water flow experiments to capture the spatial flow information. Based on the well-established recurrence network theory, we develop a novel multiplex multivariate recurrence network (MMRN) to fully and comprehensively fuse our double-layer multi-channel signals. Then we derive the projection networks from the inferred MMRNs and exploit the average clustering coefficient and the spectral radius to quantitatively characterize the nonlinear recurrent behaviors related to the distinct flow patterns. We find that these two network measures are very sensitive to the change of flow states and the distributions of network measures enable to uncover the spatial dynamical flow behaviors underlying different oil-water flow patterns. Our method paves the way for efficiently analyzing multi-channel signals from multi-layer sensor measurement system.