Finding common patterns is an important problem for several computer science subfields such as Machine Learning (ML) and Data Mining (DM). When we use graph-based representations, we need the Subgraph Isomorphism (SI) operation for finding common patterns. In this research we present a new approach to find a SI using a list code based representation without candidate generation. We implement a step by step expansion model with a width-depth search. The proposed approach is suitable to work with labeled and unlabeled graphs, with directed and undirected edges. Our experiments show a promising method to be used with scalable graph matching.