  In this paper we analyze the spectral gap of a weighted graph which is the
difference between the smallest positive and largest negative eigenvalue of its
adjacency matrix. Such a graph can represent e.g. a chemical organic molecule.
Our goal is to construct a new graph by bridging two given weighted graphs over
a bipartite graph. The aim is to maximize the spectral gap with respect to a
bridging graph. To this end, we construct a mixed integer semidefinite program
for maximization of the spectral gap and compute it numerically.
