Surveillance of antimicrobial resistance (AMR) is an important component of public health. Antimicrobial drug use generates selective pressure that may lead to resistance against to the administered drug, and may also select for collateral resistances to other drugs. Analysis of AMR surveillance data has focused on resistance to individual drugs but joint distributions of resistance in bacterial populations are infrequently analyzed and reported. New methods are needed to characterize and communicate joint resistance distributions. Markov networks are a class of graphical models that define connections, or edges, between pairs of variables with non-zero partial correlations and are used here to describe AMR resistance relationships. The graphical least absolute shrinkage and selection operator is used to estimate sparse Markov networks from AMR surveillance data. The method is demonstrated using a subset of Escherichia coli isolates collected by the National Antimicrobial Resistance Monitoring System between 2004 and 2012 which included AMR results for 16 drugs from 14418 isolates. Of the 119 possible unique edges, 33 unique edges were identified at least once during the study period and graphical density ranged from 16.2% to 24.8%. Two frequent dense subgraphs were noted, one containing the five β-lactam drugs and the other containing both sulfonamides, three aminoglycosides, and tetracycline. Density did not appear to change over time (p = 0.71). Unweighted modularity did not appear to change over time (p = 0.18), but a significant decreasing trend was noted in the modularity of the weighted networks (p < 0.005) indicating relationships between drugs of different classes tended to increase in strength and frequency over time compared to relationships between drugs of the same class. The current method provides a novel method to study the joint resistance distribution, but additional work is required to unite the underlying biological and genetic characteristics of the isolates with the current results derived from phenotypic data.