In this article, we present the Construction Grammar Conceptual Network method, developed for identifying lexical similarity and word sense discrimination in a syntactically tagged corpus, based on the cognitive linguistic assumption that coordination construction instantiates conceptual relatedness. This graph analysis method projects a semantic value onto a given coordinated syntactic dependency and constructs a second-order lexical network of lexical collocates with a high co-occurrence measure. The subsequent process of clustering and pruning the graph reveals lexical communities with high conceptual similarity, which are interpreted as associated senses of the source lexeme. We demonstrate the theory and its application to the task of identifying the conceptual structure and different meanings of nouns, adjectives and verbs using examples from different corpora, and explain the modulating effects of linguistic and graph parameters. This graph approach is based on syntactic dependency processing and can be used as a complementary method to other contemporary natural language processing resources to enrich semantic tasks such as word disambiguation, domain relatedness, sense structure, identification of synonymy, metonymy, and metaphoricity, as well as to automate comprehensive meta-reasoning about languages and identify cross/intra-cultural discourse variations of prototypical conceptualization patterns and knowledge representations. As a contribution, we provide a web-based app at http://emocnet.uniri.hr/.