There are several approaches to lower the complexity of huge networks. One of the key notions is that of twin nodes, exhibiting the same connection pattern to the rest of the network. We extend this idea by defining a twin preserving spanning subgraph (TPS-subgraph) of a simple graph as a tool to compute certain graph related invariants which are preserved by the subgraph. We discuss how these subgraphs preserve some distance based parameters of the simple graph. We introduce a sub-skeleton graph on a vector space and examine its basic properties. The sub-skeleton graph is a TPS-subgraph of the non-zero component graph defined over a vector space. We prove that some parameters like the metric-dimension are preserved by the sub-skeleton graph.

中文翻译：

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关于双保跨子图

有几种降低大型网络复杂性的方法。关键概念之一是双节点，它与网络的其余部分具有相同的连接模式。我们通过定义简单图的孪生保留跨越子图（TPS-subgraph）作为一种工具来计算该子图保留的某些图相关不变量，从而扩展了该思想。我们讨论这些子图如何保留简单图的一些基于距离的参数。我们在向量空间上引入一个子骨架图，并检查其基本特性。子骨架图是在向量空间上定义的非零分量图的TPS子图。我们证明子骨架图保留了某些参数（如度量维度）。