Analysis of a network in terms of vulnerability is one of the most significant problems. Graph theory serves as a valuable tool for solving complex network problems, and there exist numerous graph-theoretic parameters to analyze the system's stability. Among these parameters, the closeness parameter stands out as one of the most commonly used vulnerability metric. Its definition has evolved over time to enhance ease of formulation and applicability to disconnected structures. Furthermore, based on the closeness parameter, residual closeness, which is a newer and more sensitive parameter compared to other existing parameters, has been introduced as a new graph vulnerability index by Dangalchev. In this study, the outcomes of the closeness and residual closeness parameters in Harary Graphs have been examined. Harary Graphs are well-known constructs that are distinguished by having $n$ vertices that are $k$-connected with the least possible number of edges.

翻译：网络脆弱性分析是至关重要的问题之一。图论为解决复杂网络问题提供了有力工具，并存在多种基于图论的参数用于分析系统稳定性。其中，接近度参数是最常用的脆弱性度量指标之一。为简化公式表达并提升对非连通结构的适用性，其定义已历经演变。此外，Dangalchev基于接近度参数引入了剩余接近度——一种相较于现有参数更新颖且更敏感的图脆弱性指标。本研究探讨了哈拉里图中接近度与剩余接近度参数的特性。哈拉里图作为经典图结构，其独特之处在于以最少边数实现$n$个顶点的$k$-连通性。