Concentration properties of semi-vertex transitive graphs and random bi-coset graphs

TL;DR

This paper demonstrates that random bi-coset graphs are almost always concentrators and provides examples of semi-vertex transitive concentrators, highlighting their importance in network design.

Contribution

It proves the high-probability concentrator property of random bi-coset graphs and constructs explicit semi-vertex transitive concentrators.

Findings

Random bi-coset graphs are almost always concentrators

Explicit examples of semi-vertex transitive concentrators are constructed

Concentrators are crucial for efficient switching network design

Abstract

It is well-known that concentrators are sparse graphs of high connectivity, which play a key role in the construction of switching networks; and any semi-vertex transitive graph is isomorphic to a bi-coset graph. In this paper, we prove that random bi-coset graphs are almost always concentrators, and construct some examples of semi-vertex transitive concentrators.