Totally Unimodular Node–Arc Incidence Matrices: Medium Collection A (1000 - 20,000 nodes)

This dataset contains a collection of totally unimodular (TU) node–arc incidence matrices, generated from random directed graphs with node counts between 1000 and 20 000. 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 benchmarking medium-sized network flow and minimum-cost flow solvers, and studying algorithmic scalability.