MATLAB Implementation of Assortativity Coefficient with Algorithm Explanation

The Assortativity Coefficient is a crucial metric for measuring connection preferences between nodes in complex networks, particularly used to analyze whether highly connected nodes tend to link with other highly connected nodes (assortativity) or with low-degree nodes (disassortativity). Its value ranges from [-1, 1], where positive values indicate assortativity, negative values represent disassortativity, and values near zero suggest no significant connection preference in the network.

The core implementation logic in MATLAB can be divided into the following steps: Network Topology Data Acquisition: Typically input network structure as adjacency matrix or edge list format. In adjacency matrices, element values of 1 indicate connections between nodes, while 0 represents no connection. Node Degree Calculation: Count the number of connections per node (i.e., degree), stored as a vector. For directed networks, distinguish between in-degree and out-degree using MATLAB's `sum` function along different dimensions (e.g., `sum(A,1)` for in-degree, `sum(A,2)` for out-degree). Edge Information Extraction: Iterate through all edges using `find` function or sparse matrix operations, record degree values of both end nodes for each edge, forming two corresponding degree sequences. Pearson Correlation Coefficient Calculation: Compute linear correlation coefficient for the two degree sequences using MATLAB's built-in `corr` function, which directly yields the assortativity coefficient. The implementation would be: `r = corr(degree_seq1, degree_seq2)`.

Important Considerations: For undirected networks, each edge should be recorded only once to avoid duplication using triangular matrix indexing or unique edge identification. If the network contains isolated nodes (degree 0), preprocess by removing them using logical indexing (`degrees > 0`) to prevent invalid calculations. For large-scale networks, utilize sparse matrix storage (`sparse()`) and optimized algorithms to enhance computational efficiency through vectorized operations.

The assortativity coefficient finds applications in social network analysis (typically assortative), biological networks (often disassortative), and serves as a fundamental tool for understanding the relationship between network topology and functionality through quantitative correlation measurement.