The Internet of Things (IoT) performs intensive and varied communications by a large number of devices will be overwhelmed shortly. These devices are expected to provide millions of known services and other new services. This may result in several implications for scalability, navigability, and trustworthiness. That is, it may become challenging for a device to reach an appropriate service provided by other devices. Recently a new paradigm known as the Social Internet of Things (SIoT) has gained momentum with many researchers working towards incorporating social networking concepts into IoT. By utilizing SIoT concepts, humans’ innate ability to discover, select, and use services in social networks can be extended to devices participating in IoT networks. In this context, the benchmark dataset for SIoT, namely the Santander city dataset is being adopted by many researchers for validating their proposals. In this paper, an attempt has been made to analyze the Santander dataset using a graph theoretic approach based on the Local Network Structure (LNS) i.e., node or vertex characteristics namely centrality measures. The novelty in this work can be ascribed to the application of the graph theoretic approach to large networks or graphs and get hindsight of certain intrinsic properties of large real-time networks. The major centrality measures considered in this work are degree centrality, eigen Katz centrality, vector centrality, closeness, page rank, and betweenness centralities. The integration of social networking concepts into IoT enhances service discovery, trust management, and scalability by enabling autonomous device relationships, improving network navigability, optimizing resource allocation, and strengthening security. It is observed that the outcome of the experiment provides clear insights into the efficacy of different social relationships on the aforesaid metrics using Local or Node Level analysis say, the Ownership Object Relationship (OOR) relationship displays significant node degree (43.68%). Moreover, the Co-Location Object Relationship (CLOR) relationship exhibits the highest betweenness centrality (85.6%), while the effectiveness of closeness centrality is demonstrated in three relationships: OOR (28.00%), Social Object Relationship (SORv1) (24.14%), and SORv2 (24.45%).

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