Structural understanding of natural language requires explicit recovery of internal meaning structures (entities, facts, nested relations), yet current structural-analytic tasks are fragmented by inconsistent task requirements across datasets. We investigate the problem of robust cross-task structural understanding under heterogeneous requirements across structural-analytic tasks and outline a perspective called Analytic NLP in which tasks can be reformulated into a representation-then-decision paradigm. In this paper, we suggest a solution for the representation layer, called Lingua-Graph, which explicitly captures entities, facts, and relations. By representing predictions as explicit graphs with labeled nodes and edges, Lingua-Graph also improves interpretability, enabling transparent inspection and error analysis of intermediate meaning structures. We construct a labeled Lingua-Graph dataset and train a baseline parser. Experiments show that Lingua-Graph provides substantially higher entity-structure hostability than alternative representations on average, and OpenIE systems based on Lingua-Graph achieve superior performance on three benchmarks, demonstrating that better intermediate structures translate into downstream gains. The data, code and the trained model are publicly released at https://github.com/rudaoshi/Lingua.