## Modulus on graphs as a generalization of standard graph theoretic quantities

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- by Nathan Albin, Megan Brunner, Roberto Perez, Pietro Poggi-Corradini and Natalie Wiens PDF
- Conform. Geom. Dyn.
**19**(2015), 298-317 Request permission

## Abstract:

This paper presents new results for the modulus of families of walks on a graph—a discrete analog of the modulus of curve families due to Beurling and Ahlfors. Particular attention is paid to the dependence of the modulus on its parameters. Modulus is shown to generalize (and interpolate among) three important quantities in graph theory: shortest path, effective resistance, and max-flow or min-cut.## References

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## Additional Information

**Nathan Albin**- Affiliation: Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, Kansas 66506
- Email: albin@math.ksu.edu; pietro@math.ksu.edu
- Received by editor(s): June 1, 2015
- Received by editor(s) in revised form: October 30, 2015
- Published electronically: December 4, 2015
- Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. 126287 (Albin, Brunner, Perez, Wiens), through Kansas State University’s 2014 Summer Undergraduate Mathematics Research program, and under Grant Nos. 1201427 (Poggi-Corradini) and 1515810 (Albin)
- © Copyright 2015 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**19**(2015), 298-317 - MSC (2010): Primary 90C35
- DOI: https://doi.org/10.1090/ecgd/287
- MathSciNet review: 3430866