Computation of structural parameters of a collaboration graph from social networks

Abstract

Mathematicians and Sociologists are analyzing a social network from the perspective of both quality and quantity. To identify a network structure, it is pertinent to know not only every individual in the network, but also his/her role. In such networks, we fix one individual and probe all his contacts with reference to a specific relation. Here, we take up for our investigation, one such social network called Rolf Nevanlinna Prize Winners academic research collaboration network.Follow the procedure given in Appendix-1 to peruse the data available in Mathematical Reviews-MR of American Mathematical Society-AMS website and find the Erdos Numbers-ENs of Rolf Nevanlinna Prize Winners-RNPWs and their links to Erdos through various levels as per their Erdos Numbers to generate the RNPWs Collaboration Graph-RNPWCG. (Erdos is at Level 0; Direct co-authors of Erdos are at Level 1; Co-authors to the direct co-authors of Erdos are at Level 2 and so on). Investigate balanced graphs and devise procedures for obtaining various structural parameters like, tuner sets, positive influence dominating sets, obtain general results concerning 2-dominating sets for any graph G, computation of various domination numbers of RNPWCG.We have (a) derived bounds for parameters such as top, gap for balanced and non-balanced sets, (b) exact values of domination parameters given above and (c) the Tuner sets for the Rolf Nevanlinna Prize Winners collaboration graph for the period 1982–2006 for illustrative purposes. Further, in addition to recording the motivational factors for this work we also list a number of open problems for further study.We are able to determine the role, position and contribution of every individual in the social interaction academic research collaboration network of mathematicians related to the Rolf Nevanlinna Prize winners.