Biological networks, which are generally wide complicated networks, contain important information. Regarding to their remarkable growth, in order to extract their information, different works are done on them. Among the most important is to find network motifs. Motif is defined as the patterns of interactions that are observed in the given network more frequently than random networks. Studies have shown that these patterns are functionally significant. So far many algorithms have been proposed for finding subgraphs with high frequency in unweighted networks but they suffer from two essential limitations. First, most of the proposed methods are capable of finding motifs in unweighted networks. Regarding to networks’ growth in recent decade, studying other characteristics such as the nature of the coupling between edges’ weights which is beyond the topological characteristics of networks, is of great importance. Studying weighted networks instead of unweighted networks let us examine the coupling between edges weights. One of the main reasons for the lack of such studies is that considering edge weight poses novel computational challenges. Another limitation of the most current motif finding techniques is that they only consider induced subgraphs in counting subgraphs. Counting the non-induced occurrences of the network motifs is not only challenging but also quite desirable as available protein-protein interaction networks are far from complete and error free. The reported interactions by these networks include many false interactions and miss many others. An occurrence of a specific network motif in one network may include additional edges in its occurrence in another network and vice versa. One of the problems which hinders the pattern analysis of graphs is that they are neither vectorial in nature nor easily transformed into vectors. In this thesis a novel method is proposed to overcome the two shortcomings of the previous methods. Unlike the previous methods that use isomorphism (exact matching) in order to assign the found subgraphs into similar groups, the proposed method use inexact graph matching. Using inexact graph matching in available protein-protein interaction networks that have high error is quite desirable. The proposed method introduces consensus motifs in which each edge weight shows the expected probability of its presence in the consensus motif. It takes advantages of symmetrical polynomial in order to construct spectral features of subgraphs. Then it analyses and matches the resulting feature vectors by clustering instead of left; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr" dir=ltr align=left Keywords: weighted protein-protein interaction networks, weighted motif, inexact graph matching, non-induced subgraph, subgraph spectral feathers, clustering.