  A new heuristic based on vertex invariants is developed to rapidly
distinguish non-isomorphic graphs to a desired level of accuracy. The method is
applied to sample subgraphs from an E.coli protein interaction network, and as
a probe for discovery of extended motifs. The network's structure is described
using statistical properties of its $N$-node subgraphs for $N\leq 14$. The Zipf
plots for subgraph occurrences are robust power laws that do not change when
rewiring the network while fixing the degree sequence -- although the specific
subgraphs may exchange ranks. However the exponent depends on $N$. The study of
larger subgraphs highlights some striking patterns for various $N$. Motifs, or
connected pieces that are over-abundant in the ensemble of subgraphs, have more
edges, for a given number of nodes, than antimotifs and generally display a
bipartite structure or tend towards a complete graph. In contrast, antimotifs,
which are under-abundant connected pieces, are mostly trees or contain at most
a single, small loop. The extension to directed graphs is straightforward.
