Analyzing conducting rod networks using centrality

Abstract

Recently, transparent conductive films made of metallic nanowires have been closely studied owing to their excellent optoelectric and mechanical performance. Microstructures inside the films are made up of intricate networks composed of nanoscale conducting rods, and the electrical performance of the film is determined by these structures. Therefore, it has become necessary to quantify their macro- and/or micro-structural information using reasonable indicators, which could be used as metrics for optimizing film performance. In this study, a network was modeled using a multi-nodal representation and was converted into an equivalent circuit using the Laplacian eigenmap. Using the Laplacian eigenmap, internal and junction resistances can be clearly visualized, the main backbone distinguished from dangling loops, and the importance of nodes investigated. To extract structural information, we applied the concept of centrality, where betweenness centrality (β), closeness centrality (γ), and degree centrality (δ) were considered. We also introduced representative centralities for a given network, which not only correlated with the conductivity of the network but can also be used as a quantitative indicator.