In this thesis, we consider the non-bipartite property of a graph. The basic characterization of non-bipartivity says that a graph is bipartite if and only if it does not contain cycles of odd length. But, not all graphs are equally far from being bipartite. To be able to measure how far a graph is from being bipartite, we define four different non-bipartivity measures, all of whom achieve values between 0 and 1. The first measure is based on the ratio of the number of frustrated edges to the total number of edges in a graph. We calculate this measure approximately, using the properties of the signless Laplacian matrix. The second measure is based on the distance between the smallest and the largest eigenvalues of the adjacency matrix, while the third measure is based on the distance between the smallest and the largest eigenvalues of the normalized adjacency matrix. The final measure is based on the ratio of the number of odd cycles to the total number of all cycles in a graph, and we calculate it using the properties of the adjacency matrix. Using Mathematica we are able to test the defined measures and observe how their values change for some known classes of graphs - complete graphs, cycles, stars, and generalized Petersen graphs.