Network Construction from Time Series Using Visibility Graph Theory

This article introduces the methodology of constructing complex networks from time series using visibility graph theory. Complex networks consist of numerous nodes and edges, where each node represents an object and each edge signifies a connection between two objects. This network construction approach finds applications in various domains such as social networks, biological networks, and transportation networks. The core algorithm involves converting time series data points into network nodes, where visibility lines between data points form the edges - two data points are connected if they can "see" each other without being obstructed by intermediate points. After generating the network, we calculate its clustering coefficient to evaluate the degree of node clustering within the network. The clustering coefficient serves as a crucial metric for measuring how closely nodes tend to cluster together, revealing the density of connections among neighboring nodes. Through analysis of these network properties, we can gain deeper insights into network topology and inter-node relationships, thereby providing valuable information for research applications. Implementation typically involves creating adjacency matrices from visibility conditions and using network analysis libraries to compute graph metrics.