The concepts of centrality and diversity are highly important in search algorithms, and play central roles in applications of artificial intelligence (AI), machine learning (ML), social networks, and pattern recognition. This work examines the significance of centrality and diversity in representation, regression, ranking, clustering, optimization, and classification. The text is designed to be accessible to a broad readership. Requiring only a basic background in undergraduate-level mathematics, the work is suitable for senior undergraduate and graduate students, as well as researchers working in machine learning, data mining, social networks, and pattern recognition. .