Complex Network Basic Parameters: Clustering Coefficient Calculation

Complex networks refer to networks composed of a large number of nodes and connections. The fundamental parameters of complex networks include node count, connection number, average degree, among others. The clustering coefficient is a crucial metric used to measure the degree of node clustering within a network, calculated by examining the number of connections between neighboring nodes.

From an implementation perspective, calculating the clustering coefficient typically involves analyzing the local connectivity structure around each node. For undirected networks, the clustering coefficient for a node can be computed using the formula: C_i = (2 * e_i) / (k_i * (k_i - 1)), where e_i represents the number of existing edges between the node's neighbors, and k_i denotes the degree of the node. A common algorithmic approach involves iterating through all nodes, identifying their neighbors, and counting the actual connections between these neighbors. In Python, libraries like NetworkX provide built-in functions such as nx.clustering(G) for efficient computation, while MATLAB implementations might utilize adjacency matrix operations and neighbor intersection calculations. The global clustering coefficient can be obtained by averaging all local coefficients or by using the triplets method (3 * number of triangles / number of connected triples).