Frequent itemset mining is an established data mining technique focused on discovering recurrent item combinations from transactional data. The extraction process can be modelled as an exploration of a lattice representing high-order item relations and is typically driven by ad hoc quality metrics (e.g., the support index). The exploration of the candidate item relations can be addressed using established graph generalization, called simplicial complexes. This thesis work analyzes the similarities between simplicial complexes and frequent itemsets, discusses the formal relations between them, and prospects for new and more advanced synergies between topological analyses and pattern mining techniques.