Colexification in comparative linguistics refers to the phenomenon of a lexical form conveying two or more distinct meanings. In this paper, we propose simple and effective methods to build multilingual graphs from colexification patterns: ColexNet and ColexNet+. ColexNet's nodes are concepts and its edges are colexifications. In ColexNet+, concept nodes are in addition linked through intermediate nodes, each representing an ngram in one of 1,334 languages. We use ColexNet+ to train high-quality multilingual embeddings $\overrightarrow{\mbox{ColexNet+}}$ that are well-suited for transfer learning scenarios. Existing work on colexification patterns relies on annotated word lists. This limits scalability and usefulness in NLP. In contrast, we identify colexification patterns of more than 2,000 concepts across 1,335 languages directly from an unannotated parallel corpus. In our experiments, we first show that ColexNet has a high recall on CLICS, a dataset of crosslingual colexifications. We then evaluate $\overrightarrow{\mbox{ColexNet+}}$ on roundtrip translation, verse retrieval and verse classification and show that our embeddings surpass several baselines in a transfer learning setting. This demonstrates the benefits of colexification for multilingual NLP.