  Triadic analysis encompasses a useful set of graph mining methods that are
centered on the concept of a triad, which is a subgraph of three nodes. Such
methods are often applied in the social sciences as well as many other diverse
fields. Triadic methods commonly operate on a triad census that counts the
number of triads of every possible edge configuration in a graph. Like other
graph algorithms, triadic census algorithms do not scale well when graphs reach
tens of millions to billions of nodes. To enable the triadic analysis of
large-scale graphs, we developed and optimized a triad census algorithm to
efficiently execute on shared memory architectures. We then conducted
performance evaluations of the parallel triad census algorithm on three
specific systems: Cray XMT, HP Superdome, and AMD multi-core NUMA machine.
These three systems have shared memory architectures but with markedly
different hardware capabilities to manage parallelism.
