Random Simple Undirected Weighted Graphs

Dataset Description

We introduce a dataset consisting of over 60 flow matrices representing simple, undirected, weighted graphs. This dataset is designed to support empirical studies in graph algorithms, clustering, and network analysis.

Each graph is characterized by

• Order (|V|):
  {20, 50, 100, 300, 500, 700, 800, 900, 1000, 2000, 3000}

• Density:
  For each graph order, 10 instances are generated with edge densities from the following set:
  {0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 1.0}

• Clustered Structure:
  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.

• Number of Clusters:
  The number of clusters varies according to graph order:
  {5, 5, 10, 30, 50, 70, 80, 90, 100, 400, 500}

This dataset enables systematic testing of algorithms under varying structural conditions, including scale, sparsity, and community strength.