Computational Tools for Complex Networks: Clustering Coefficient and Average Clustering Coefficient Functions

Computational tools for complex networks, specifically functions for calculating clustering coefficient and average clustering coefficient. These functions serve as essential tools for analyzing and evaluating connection patterns and clustering degrees among nodes in complex networks. The clustering coefficient represents the probability that neighbors of a node are connected to each other, while the average clustering coefficient is the mean value of clustering coefficients across all nodes in the entire network. Through computing these coefficients, we can understand the network's clustering degree and connection patterns between nodes, thereby gaining better insights into complex network characteristics and behaviors. In implementation, the clustering coefficient function typically requires adjacency matrix input and calculates for each node the ratio of existing edges between its neighbors to all possible edges among them. The average clustering coefficient function then aggregates these individual values using mean calculation. Key algorithmic considerations include efficient neighbor identification and edge counting methods, often optimized for sparse matrix operations in large-scale networks. These functions commonly employ graph theory libraries and may include parameters for handling directed/undirected networks and weighted edges.