Random Simple Undirected Weighted Graphs

<div> <div> <div> <div> <div> <div dir="auto"> <div> <div> <h3>Dataset Description</h3> <p>We introduce a dataset consisting of <em><strong>over 60 flow matrices</strong></em> representing <strong>simple</strong>, <strong>undirected</strong>, <strong>weighted</strong> <strong>graphs</strong>. This dataset is designed to support empirical studies in graph algorithms, clustering, and network analysis.</p> <p>Each graph is characterized by</p> <ul> <li> <p><strong>Order (|V|):</strong><br><span><span>{20, 50, 100, 300, 500, 700, 800, 900, 1000, 2000, 3000}</span></span></p> </li> <li> <p><strong>Density:</strong><br>For each graph order, 10 instances are generated with edge densities from the following set:<br><span><span>{0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 1.0}</span></span></p> </li> <li> <p><strong>Clustered Structure:</strong><br>Nodes are partitioned into predefined clusters, where intra-cluster edges have significantly higher weights, while all inter-cluster edges are uniformly weighted (weight = 1). This structure simulates modular graphs commonly encountered in real-world networks.</p> </li> <li> <p><strong>Number of Clusters:</strong><br>The number of clusters varies according to graph order:<br><span><span>{5, 5, 10, 30, 50, 70, 80, 90, 100, 400, 500}</span></span></p> </li> </ul> <p>This dataset enables systematic testing of algorithms under varying structural conditions, including <strong>scale</strong>, <strong>sparsity</strong>, and <strong>community strength.</strong></p> </div> </div> </div> </div> </div> </div> </div> </div> <div> <div> <div> <div> <div> <div dir="auto"> <div> <div> <p>&nbsp;</p> </div> </div> </div> </div> </div> </div> </div> </div>