  We present a novel graph embedding space (i.e., a set of measures on graphs)
for performing statistical analyses of networks. Key improvements over existing
approaches include discovery of "motif-hubs" (multiple overlapping significant
subgraphs), computational efficiency relative to subgraph census, and
flexibility (the method is easily generalizable to weighted and signed graphs).
The embedding space is based on {\it scalars}, functionals of the adjacency
matrix representing the network. {\it Scalars} are global, involving all nodes;
although they can be related to subgraph enumeration, there is not a one-to-one
mapping between scalars and subgraphs. Improvements in network randomization
and significance testing--we learn the distribution rather than assuming
gaussianity--are also presented. The resulting algorithm establishes a
systematic approach to the identification of the most significant scalars and
suggests machine-learning techniques for network classification.
