Strongly Regular Multigraphs

A family of regular graphs which have a direct connection to structures in algebraic combinatorics are strongly regular graphs. These graphs are defined by 4 parameters, n, k, a, and c, where n is the number of nodes, k is the degree of each node, a is the number of common neighbors for every adjacent pair of nodes, and c is the number of common neighbors for every nonadjacent pair of nodes. A multigraph is a graph that has no self-loops, but may have multiple edges and is formally defined by specifying a graph G and assigning a multiplicity to each edge of G. We examine underlying strongly regular multigraphs in order to further clarify their properties, specifically with regard to combinatorial configurations.