Calculating Node Degrees, Degree Distribution, and Betweenness Centrality in Directed Weighted Networks

Before calculating node degrees, degree distribution, and betweenness centrality for directed weighted networks, it is essential to conduct a comprehensive analysis and understanding of the network structure. This includes examining the number of nodes, connection patterns between nodes, directionality of connections, and edge weights. Through such analysis, we can better comprehend the network's architecture and characteristics, providing a more accurate and thorough foundation for subsequent computations. When calculating node degrees, both in-degree and out-degree must be considered. The total degree of a node is obtained by summing its incoming and outgoing connections. In code implementation, this typically involves processing the adjacency matrix where in-degree equals the sum of corresponding column elements and out-degree equals the sum of corresponding row elements. For weighted networks, degree calculation may involve summing edge weights rather than simple connection counts. For degree distribution analysis, statistical examination of all node degrees is required to understand the distribution pattern and range of degree values across the network. This often involves creating frequency histograms or probability distributions, which can be implemented using histogram functions or statistical packages in programming environments. Beyond degree calculations, betweenness centrality for directed weighted networks must be computed. Betweenness centrality identifies nodes that play crucial roles in information flow and connectivity between different network components. These nodes serve as important bridges for communication and network connectivity. Calculating betweenness centrality is vital for understanding network structure and characteristics, providing accurate and useful information for subsequent analysis and decision-making. The algorithm typically involves finding shortest paths between all node pairs (using modified Dijkstra's algorithm for weighted networks) and counting how many paths pass through each node.