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This book focuses on the computational aspects of graph convexity, with a particular emphasis on path convexity within graphs. It provides a thoughtful introduction to this emerging research field, which originated by adapting concepts from convex geometry to combinatorics and has experienced substantial growth. The book starts with an introduction of fundamental convexity concepts and then proceeds to discuss convexity parameters. These parameters fall into two categories: one derived from abstract convexity studies and another motivated by computational complexity. Subsequent chapters...