The interconnections between graph theory and algebraic structure theory have always led to innovative solutions to problems in both areas, as well as new research topics in Mathematics and other scientific fields. This reprint aims to gather a variety of novel theoretical aspects and practical applications regarding these two research areas. It contains 10 articles and a review paper selected for publication in the Special Issue, "Algebraic Structures and Graph Theory, 2nd Edition", printed by the MDPI journal Mathematics.

The topics addressed by the manuscripts within this reprint cover different aspects that are principally related to graphs constructed from lattices, semigroups, or groups, particular types of graphs (as edge-primitive, friendship, or equitable graphs), and hypercompositional algebras (HX-groups and multi-rings).