Modeling is an integral part of many computing-related disciplines and thus also represents a curricular core component in computing education in tertiary education. Competence models in which modeling is integrated at least to some extent already exist in some of these disciplines. However, for the core component of graphical modeling, a competence model that illuminates the relevant competences in detail is still lacking. Therefore, we develop a competence model for graphical modeling with the aim to make teaching and especially assessments in the field more competence-oriented. This article reports on the first two studies conducted to develop and validate the competence model for graphical modeling. In the first study, the structure of the competence model was developed based on theories and approaches of educational science. Competences relevant for graphical modeling were deductively derived from literature and existing university course descriptions using techniques of qualitative content analysis. The result of the first study is a preliminary competence model. In the second study, the preliminary competence model was reviewed by means of an expert rating in the modeling community. The competence model was revised and refined based on these findings and subsequent expert discussions. The main result of the investigation represents the competence model for graphical modeling, which includes a total of 74 competence facets at different cognitive process levels in the five content areas of "model understanding and interpreting," "model building and modifying," "values, attitudes, and beliefs," "metacognitive knowledge and skills," and "social-communicative skills."