Abstract
Topological indices describe mathematical invariants of molecules in mathematical chemistry. M-polynomials of chemical graph theory have freedom about the nature of molecular graphs and they play a role as another topological invariant. Social networks can be both cyclic and acyclic in nature. We develop a novel application of M-polynomials, the ( m , n , r ) -agent recruitment graph where n > 1 , to study the relationship between the Dunbar graphs of social networks and the small-world phenomenon. We show that the small-world effects are only possible if everyone uses the full range of their network when selecting steps in the small-world chain. Topological indices may provide valuable insights into the structure and dynamics of social network graphs because they incorporate an important element of the dynamical transitivity of such graphs.
Highlights
Social networks have become a topic of major interest in recent years
We can determine the topological indices for a set of graphs that differ in their size and structure in the way we suggested in the Introduction
We have shown that it is possible to describe the properties of networks using invariants from chemical graph theory
Summary
Social networks have become a topic of major interest in recent years. Many studies have focused on the size and structure of ego-centric networks (the world as seen from the individual’s perspective) rather than taking a top-down overview of the global network as a while. The six degrees of separation observed by Milgram [14] and others in offline networks may reflect the cognitive limits that prevent humans searching through all possible paths This is likely to be because humans will usually only be aware of the people in their immediate, personal social network. They will assume that each of those people in turn has a network they can reach out to at each successive step, the initiator does not have any knowledge of those networks, and may make poor choices Given these two very different ways of looking at social networks, an obvious question is how the small-world constants map onto Dunbar graphs. One may refer [40,41,42,43,44,45,46,47,48,49,50,51] for some extensive works related to above directions
Sign-in/Register to view highlights & summary 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.
