Convex optimization techniques can be applied to many problems. In this exercise we investigated algebraic connectivity of graphs. First, we formulated the problem of finding edge weights that maximize algebraic connectivity as a convex optimization problem. And second, we used a numerical example to calculate and compare the algebraic connectivity of a graph with optimal edge weights versus uniform constant edge weights. We concluded that optimal edge weights lead to better algebraic connectivity, because important edges carry greater weight and therefore, significantly improve the overall graph connectivity. Using this numerical example we demonstrated that greater number of edges does not necessarily lead to greater algebraic connectivity. Instead, optimal edge weights are more important.
