Bounds for the global cyclicity index of a general network via weighted majorization

In this paper we define a new graph-theoretic cyclicity index CW(G) as a natural generalization of the global cyclicity index C(G) when arbitrary resistances are allocated to each edge of an electrical network. Upper and lower bounds for CW(G) are then provided using a powerful technique, based on p-majorization which extends our prior studies. These new results on weighted majorization are of interest in themselves and may be applied also in other scenarios.