Semantic graphs, such as WordNet, are resources which curate natural language on two distinguishable layers. On the local level, individual relations between synsets (semantic building blocks) such as hypernymy and meronymy enhance our understanding of the words used to express their meanings. Globally, analysis of graph-theoretic properties of the entire net sheds light on the structure of human language as a whole. In this paper, we combine global and local properties of semantic graphs through the framework of Max-Margin Markov Graph Models (M3GM), a novel extension of Exponential Random Graph Model (ERGM) that scales to large multi-relational graphs. We demonstrate how such global modeling improves performance on the local task of predicting semantic relations between synsets, yielding new state-of-the-art results on the WN18RR dataset, a challenging version of WordNet link prediction in which “easy” reciprocal cases are removed. In addition, the M3GM model identifies multirelational motifs that are characteristic of well-formed lexical semantic ontologies.