Overlapping Neighborhood in Graph

Overlapping neighborhoods in graphs capture the extent to which nodes share common connections, revealing hidden communities, influence patterns, and functional similarities within complex networks. However, identifying and analyzing these overlaps is challenging due to a small network, heterogeneity, noise, and the dynamic nature of real-world graph data. This chapter explores the concepts of overlapping neighborhoods in graphs. It starts with the definition and pointing out its need in similarity analyses, and connectivity among nodes. It also adds the idea of local and global overlap measures, including Jaccard similarity, Adamic-Adar, Katz index, SimRank, and PageRank-based similarity. The next section talks about the different visualization types to interpret overlapping structures effectively. Neighborhood overlapping concepts that support community detection, recommendation systems, and relationship analysis are demonstrated by using real-time use cases from healthcare and social networks.