Proteins are important biomolecules, which perform diverse structural and functional roles in living systems. Starting from a linear chain of amino acids, proteins fold to different secondary structures, which then fold through short- and long-range interactions to give rise to the final three-dimensional shapes useful to carry out the biophysical and biochemical functions. Proteins are defined as having a common `fold' if they have major secondary structural elements with same topological connections. It is known that folding mechanisms are largely determined by a protein's topology rather than its interatomic interactions. The native state protein structures can, thus, be modelled, using a graph-theoretical approach, as coarse-grained networks of amino acid residues as `nodes' and the inter-residue interactions/contacts as `links'. Using the network representation of protein structures and their 2D contact maps, we have identified the conserved contact patterns (groups of contacts) representing two typical folds – the EF-hand and the ubiquitin-like folds. Our results suggest that this direct and computationally simple methodology can be used to infer about the presence of specific folds from the protein's contact map alone.