Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Node-arc incidence matrix

  • Saul I. Gass
  • Carl M. Harris
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_674

For the minimum-cost network-flow problem, this is a matrix in which the rows i correspond to the nodes and the columns j correspond to the arcs. For an arc (i, j), with its flow directed from i to j, the entry in matrix location (i, j)is a + 1 and the entry in location (j, i)is a − 1. All other entries are zero. Thus, every column has only two nonzero entries. Such matrices are unimodular.  Minimum-cost network-flow problem;  Multicommodity network flows; Network optimization.

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Saul I. Gass
    • 1
  • Carl M. Harris
    • 2
  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA