Biological networks are receiving increased attention due to their importance in understanding life at the cellular level. There exist many different kinds of biological networks, and different models have been proposed for them. In this dissertation we focus on suitable network models for representing experimental data on protein interaction networks and protein complex networks (protein complexes are groups of proteins that associate to accomplish some function in the cell), and to design algorithms for exploring such networks. Our goal is to enable biologists to identify the general principles that govern the organization of protein-protein interaction networks and protein complex networks. For protein complex networks, we propose a hypergraph model which more accurately represents the data than earlier models. We define the concept of k-cores in hypergraphs, which are highly connected subhypergraphs, and design an algorithm for computing k -cores in hypergraphs. A major challenge in computational systems biology is to understand the modular structure of biological networks. We construct computational models for predicting functional modules through the use of graph clustering techniques. The application of earlier graph clustering techniques to proteomic networks does not yield good results due to the high error rates present, and the small-world and power-law properties of these networks. We discuss the various requirements that clusterings of biological networks are required to satisfy, design an algorithm for computing a clustering, and show that our clustering approach is robust and scalable. Moreover, we design a new algorithm to compute overlapping clustering rather than exclusive clustering. Our approach identifies a set of clusters and a set of bridge proteins that form the overlap among the clusters. Finally we assess the quality of our proposed clusterings using different reference sets.