The complexity and variability of the contemporary labour markets creates the need for continuous improvement of methods used for their description, analysis and forecasting. Looking for a tool that allows for the simultaneous analysis of various aspects of contemporary labour markets, the authors focused their attention on k-partite graph models (with particular emphasis on bipartite graphs). The assessment of the usefulness of models based on bipartite graphs for analysis of regularities occurring on the Polish labour market is the main aim of the paper. The authors studied the regional distribution of the demand for employee competencies and evaluated the specificity of localities and competencies. The concept of bipartite competency schemas is also introduced in the paper. These schemas can be used as models representing strongly related competencies and localities. The usefulness of bipartite competency schemas was confirmed by empirical research presented in the paper. The content of job offers published online formed the main source of data examined. All analyses were performed with the use of the R programming language.