International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4030 2020 2020 Department of Mathematics, C.V. Raman Global University, Bhubaneswar, Odisha, India Mana Mana Department of Mathematics, C.V. Raman Global University, Bhubaneswar, Odisha, India Amaresh Chandra Panda Department of Mathematics, C.V. Raman Global University, Bhubaneswar, Odisha, India Siva Prasad Behera Department of Mathematics, Trident Academy of Technology, Bhubaneswar, Odisha, India Prasanta Kumar Raut Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand Mana Donganont Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco Said Broumi Average edge connectivity is a fundamental concept in graph theory, widely employed to evaluate the robustness of networks through the analysis of local edge cuts. Classical fuzzy extensions allow for graded membership, yet they fail to clearly distinguish between inherent uncertainty and definite absence of edges. To overcome this limitation, we introduce the notion of neutrosophic average edge connectivity, a tri-valued connectivity measure formulated within the framework of single-valued neutrosophic graphs (SVNGs). In this study, we rigorously define neutrosophic local edge cuts, establish key theoretical results including bounds and monotonicity properties, and design efficient algorithms tailored for particular families of graphs. The applicability of the proposed framework is demonstrated through a detailed communication-network case study, which highlights its capacity to capture structural resilience under indeterminate conditions. Overall, the proposed approach generalizes classical robustness indicators and provides a comprehensive tool for analyzing connectivity in networks characterized by vagueness, indeterminacy, and incomplete information. 2026 2026 167 174 10.54216/IJNS.270214 https://www.americaspg.com/articleinfo/21/show/4030