Abstract
In this paper, based on the un-weight hierarchical networks, a family of weighted hierarchical networks are introduced, the weight factor is denoted by [Formula: see text]. The weighted hierarchical networks depend on the number of nodes in complete bipartite graph, denoted by [Formula: see text], [Formula: see text] and [Formula: see text]. Assume that the walker, at each step, starting from its current node, moves to any of its neighbors with probability proportional to the weight of edge linking them. We deduce the analytical expression of the average receiving time (ART). The obtained remarkable results display two conditions. In the large network, when [Formula: see text], the ART grows as a power-law function of the network size [Formula: see text] with the exponent, represented by [Formula: see text], [Formula: see text]. This means that the smaller the value of [Formula: see text], the more efficient the process of receiving information. When [Formula: see text], the ART grows with increasing order [Formula: see text] as [Formula: see text] or [Formula: see text].
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
