In recent years, dynamic networks where the state of networks evolves in time, as individual nodes adapt to the state of the network have attracted much attention. One simple case of such an adaptive dynamics is a model of social networks in which individuals are typically comfortable with a certain number of contacts, i.e., preferred degrees. A particular limit of the latter is a system of extreme introverts and extroverts - where an introvert, given a chance, deletes one of its incoming links, and an extrovert, given a chance, adds a link to a randomly chosen introvert . Remarkably, in this case, the non-trivial exact distribution of different configurations in the steady state can be determined. The model exhibits a phase transition from very few bonds to almost all bonds present, as the ration of introvert to extroverts is varied. I will also discuss variants of the model where the agents show preferential attachment or detachment to most/ least connected of the group, which show interesting cooperative effects.
Deepak Dhar obtained his PhD in Physics from California Institute of Technology, Pasadena in 1978. Since 1978 he is associated with the Dept of Theoretical Physics at TIFR Mumbai, where he is currently a Professor. He has many awards. The list includes EP Anthony Fellowship (1972-73), RP Feynman Fellowship (1974-76), INSA Young Scientist Award (1983), SS Bhatnagar Award (1991), JR Schrieffer Prize in Condensed Matter Physics (1993), Fellow of INSA, NAS, IAS and Third World Academy of Science, SN Bose Medal of INSA (2001), Third World Academy of Science Prize in Physics (2002), Rothschild Professor (Isaac Newton Institute, 2006) and JC Bose Fellowship (2007-2017).