Assessing the interactions between time series signals using weighted horizontal visibility graphs

Abstract The visibility graph algorithm is used to map recorded time series signals to complex networks. Individual timepoints are treated as nodes, and edges are formed by some criterion of visibility between data points. Comparing two visibility graphs can facilitate assessment of the strength of interactions between the associated signals. Two existing methods for this purpose include (1) the average share of overlapping edges (average layer entanglement) between the visibility graphs and (2) the normalized mutual information (MI) between the degree distributions of the two visibility graphs. However, these methods do not always capture the full extent of interactions in some networks. Here we introduce a new approach, the community similarity score, which assesses the similarity between the structure of the communities in the visibility graphs. A community is a subset of the network where nodes are strongly connected to each other, but weakly connected to other communities. The results suggested that the community similarity score generally provided an improvement over normalized MI and average layer entanglement, achieving results that compare well to established time- and frequency-domain methods. When applied to an electroencephalography dataset, the community similarity score produced results consistent with prior literature and was robust to noise. These results suggest that our approach may provide new insights into the dynamics of complex systems and potentially serve as features in machine learning pipelines.