Totally Unimodular Node–Arc Incidence Matrices: Small Collection (50 - 1000 nodes)

This dataset contains a collection of totally unimodular (TU) node–arc incidence matrices, generated from random directed graphs with node counts between 50 and 1000. Each column of the incidence matrix has exactly one +1 (arc tail) and one –1 (arc head). Because of the TU property, all linear programming relaxations of integer flow problems are guaranteed to have integer solutions. The dataset includes: matrices.csv: sparse representation of all instances (two rows per arc, +1 and –1). metadata.csv: summary of each instance (nodes, arcs, density). Conversion scripts (make_dat_all.py, make_dat_all.R) to produce .dat files for AMPL or other solvers. Typical applications include teaching (small cases), benchmarking network flow and minimum-cost flow solvers, and studying algorithmic scalability.本数据集收录了一系列全幺模（totally unimodular, TU）节点-弧关联矩阵，这些矩阵由节点数介于50至1000之间的随机有向图生成。该关联矩阵的每一列恰好包含一个+1（代表弧的起点）与一个–1（代表弧的终点）。得益于全幺模特性，整数流问题的所有线性规划松弛问题均保证存在整数解。 本数据集包含以下内容： - matrices.csv：所有数据集实例的稀疏表示形式（每条弧对应两行，分别存储+1与–1）。 - metadata.csv：各数据集实例的汇总信息（包含节点数、弧数与密度）。 - 转换脚本（make_dat_all.py、make_dat_all.R）：用于为AMPL或其他求解器生成.dat格式文件。 其典型应用场景包括：教学演示（小型案例）、网络流与最小费用流求解器的基准测试，以及算法可扩展性研究。