\(Q\)-neutrosophic soft sets are essentially neutrosophic soft sets characterized by three independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real-life problems. Graph theory has now become a major branch of applied mathematics, and it is generally regarded as a branch of combinatorics. In this research paper, we introduce the concept of \(Q\)-neutrosophic soft graphs (Q-\({\mathcal{N}\mathcal{S}}Gs\)) that are made by combining \(Q\)-neutrosophic soft sets with graphs and describe different methods of their construction. A \(Q\)-neutrosophic soft graphs model is very much efficient for such real word problems which can construct more precise, flexible, and comparable system as compared to the classical, fuzzy and neutrosophic graph models. In this paper, we first define the concept of \(Q\)-neutrosophic soft graph (Q-\({\mathcal{N}\mathcal{S}}G\)). In this paper we introduce the concept of \(Q\)-\({\mathcal{N}\mathcal{S}}G\), strong Q-\({\mathcal{N}\mathcal{S}}G\), union and intersection of Q-\({\mathcal{N}\mathcal{S}}G\). The new concept is called Q-\({\mathcal{N}\mathcal{S}}G\) multicriteria decision-making method (Q-\({\mathcal{N}\mathcal{S}}GMCDM\) for short). Finally, we describe the utility of the \(Q\)-neutrosophic soft graph and its applications in communication network and decision-making problem.

\(Q\) -中智软集本质上是中智软集，其特征是三个独立的二维隶属函数，分别代表不确定性、不确定性和虚假性。因此，它可以应用于大多数现实生活问题中出现的二维不精确、不确定和不一致的数据。图论现已成为应用数学的一个主要分支，一般被认为是组合学的一个分支。在这篇研究论文中，我们介绍了\(Q\) - 中智软图 ( Q - \({\mathcal{N}\mathcal{S}}Gs\) ) 的概念，它们是由\(Q\) - 带有图形的中智软集并描述了它们的不同构造方法。一个\(Q\)-neutrosophic soft graphs 模型对于此类真实单词问题非常有效，与经典、模糊和中智图模型相比，它可以构建更精确、灵活和可比的系统。在本文中，我们首先定义了\(Q\) - 中智软图（Q - \({\mathcal{N}\mathcal{S}}G\)）的概念。在本文中，我们引入了\(Q\) - \({\mathcal{N}\mathcal{S}}G\) 的概念，强Q - \({\mathcal{N}\mathcal{S}}G \)，Q - \({\mathcal{N}\mathcal{S}}G\) 的并集和交集。新概念称为Q - \({\mathcal{N}\mathcal{S}}G\)多标准决策方法（简称Q - \({\mathcal{N}\mathcal{S}}GMCDM\)）。最后，我们描述了\(Q\) - 中智软图的效用及其在通信网络和决策问题中的应用。