  This paper considers the comparison between the eigenvalues of Laplace
operators with the standard conditions and the anti-standard conditions on
non-bipartite graphs which are equilateral or inequilateral. First of all, we
show the calculation of the eigenvalues of Laplace operators on equilateral
metric graphs with arbitrary edge length. Based on this method, we use the
properties of the cosine function and the arccosine function to find the
comparison between the eigenvalues of Laplace operators with the standard
conditions and the anti-standard conditions on equilateral non-bipartite
graphs. In addition, we give the inequalities between standard and
anti-standard eigenvalues on a special inequilateral non-bipartite graph.
