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Adding Neutrosophic Topological Indices to Graphs for Social Network Analysis

Author

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  • S. R. Yaseen
  • A. M. Salih
  • M. W. Alomari

Abstract

Topological indices are widely used in graph analysis under uncertainty. However, existing fuzzy and intuitionistic approaches do not fully capture indeterminacy. Neutrosophic graphs, with their truth, indeterminacy and falsity components, offer a more comprehensive framework. Despite the frequent use of the Wiener index in neutrosophic contexts, other indices remain unexplored. In this paper, we introduce two new topological indices for neutrosophic graphs: the Forgotten Topology Index FTI and the Edge Forgotten Index EDFI. We investigate their mathematical properties, including bounds, monotonicity under subgraphs and threshold behaviour, and provide rigorous proofs. We then apply these indices to evaluate the efficiency of a telecommunication network as a case study, showing how FTI and EDFI can reveal critical nodes and links under uncertainty. The proposed indices are further integrated into a simple machine learning framework to demonstrate their potential for the analysis of social networks.

Suggested Citation

  • S. R. Yaseen & A. M. Salih & M. W. Alomari, 2026. "Adding Neutrosophic Topological Indices to Graphs for Social Network Analysis," Journal of Mathematics, Hindawi, vol. 2026, pages 1-11, July.
    • Handle: RePEc:hin:jjmath:3772943
    DOI: 10.1155/jom/3772943
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