THE AVERAGE WEIGHTED PATH LENGTH FOR A CLASS OF HIERARCHICAL NETWORKS

Abstract

In this paper, in order to calculate the average path length for unweighted and weighted hierarchical networks, we define the sum of the distances from each node to the vertex and the bottom nodes. For the unweighted network, we show that the average path length grows with the size of [Formula: see text] as [Formula: see text]. For the weighted network, we prove its weighted path length approaches a constant related to the weighting factor [Formula: see text] and parameter [Formula: see text]. In particular, for [Formula: see text], the average weighted path length of the network tends to a specific value [Formula: see text].