Leonardi (2007) uses the Quadratic Assignment Procedure - QAP (Hubert & Schultz, 1976), which has also been developed further by Krackhardt (1987).
What QAP does is that it essentially takes the adjacency matrices of the two graphs that you are comparing, and then calculates Pearson correlation coefficients for each pair of matched cells (for the same set of nodes) in each adjacency matrix. It then permutes the mappings of potential edges between nodes to generate a sampling distribution, of sorts, which enables us to test for significant correlations for structural relationships.
This yields a correlation between the two graphs as wholes, with a significance value attached to it - thus enabling you to evaluate to what degree to graphs are correlated (in terms of their structure), and whether that correlation is significantly different from zero.
Hubert, L., and Schultz, J. 1976. “QUADRATIC ASSIGNMENT AS A GENERAL DATA ANALYSIS STRATEGY,” British Journal of Mathematical and Statistical Psychology (29:2), pp. 190–241.
Krackardt, D. 1987. “QAP Partialling as a Test of Spuriousness,” Social Networks (9), pp. 171–186.
Leonardi, P. 2007. “Activating the Informational Capabilities of Information Technology for Organizational Change,” Organization Science (18:5).