Triad Designs and Related Factorizations

Counting and listing triples are associated with counting and listing triangles in a graph. This is called triangle problem that has recently gained much practical importance since they are central in the so-called complex network analysis. For example, in social networks, triangles are well-studied subgraphs. Many social networks are abundant in triangles, since typically friends of friends tend to become friends themselves. This phenomenon is observed in other types of networks which have given rise to the definitions of transitivity ratio and clustering coefficients of a graph in complex network analysis. This book centered on the development of triad design on v objects, TD(v) algorithm, which is a way of arranging (Counting and listing) distinct triples of objects with several properties.