Social network analysis by Turiyam graphs

Abstract

Abstract Objective A single valued neutrosophic set represented the uncertainty of real life situations in terms of membership $$(t)$$ ( t ) , indeterminacy $$(i)$$ ( i ) and non-membership $$(f)$$ ( f ) degree. However, this uncertainty cannot be limited to those three degrees; there is also an additional refusal degree. For this issue, the Turiyam set is an appropriate tool, which described the neutrosophic refusal degree of this situation as a liberal $$(l)$$ ( l ) degree in addition to those three degrees. The graphical representation of this situation is required for knowledge processing. For this purpose, the Turiyam graph was introduced as an extension of the single valued neutrosophic graph. This graph is helpful when the depictions of the vertices or their relationships or both, are considered in terms of membership $$(t)$$ ( t ) , indeterminacy $$(i)$$ ( i ) , non-membership $$(f)$$ ( f ) and liberal $$(l)$$ ( l ) degrees. The goal of this paper is to introduce the degree, order and size in the context of Turiyam graphs and examine a social network (SN) with the help of this graph. Results In this regard, the degree, order and size in the context of Turiyam graphs are studied. The feasibility of this Turiyam graph is shown by employing its concept in a social network (SN). Finally, the advantage of the Turiyam graph over the existing graph theories is recognized by viewing its better framework.