Frank Harary (March 11, 1921 – January 4, 2005) was a prolific American mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory. Harary was a master of clear exposition and, together with his many doctoral students, he standardized the terminology of graphs. He broadened the reach of this field to include physics, psychology, sociology, and even anthropology. Gifted with a keen sense of humor, Harary challenged and entertained audiences at all levels of mathematical sophistication. A particular trick he employed was to turn theorems into games - for instance, students would try to add red edges to a graph on six vertices in order to create a red triangle, while another group of students tried to add edges to create a blue triangle (and each edge of the graph had to be either blue or red). Because of the simplest case of Ramsey theory, one team or the other would have to win.
Frank Harary was born in New York City, the oldest child to a family of Jewish immigrants from Syria and Morocco. He earned his Bachelor's and Master's degrees from Brooklyn College in 1941 and 1945 respectively and his Ph.D. from University of California at Berkeley in 1948. During 1948-1986 he was with the University of Michigan. From 1987 he was Professor (and Distinguished Professor Emeritus) in the Computer Science Department at New Mexico State University in Las Cruces. He was one of the founders of the Journal of Combinatorial Theory and the Journal of Graph Theory. He died at Memorial Medical Center in Las Cruces, New Mexico.
Harary's work in graph theory was diverse. Some topics of great interest to him were:
- Graph enumeration, that is, counting graphs of a specified kind. He coauthored a book on the subject (Harary and Palmer 1973). The main difficulty is that two graphs that are isomorphic should not be counted twice; thus, one has to apply Pólya's theory of counting under group action. Harary was an expert in this.
- Signed graphs. Harary invented this branch of graph theory, which grew out of a problem of theoretical social psychology investigated by the psychologist Dorwin Cartwright and Harary.
- Applications of graph theory in numerous areas, especially to social science. He was co-author of John Wiley's first eBook, Graph Theory and Geography.
Among over 700 scholarly articles Harary wrote, two were co-authored with Paul Erdős, giving Harary an Erdős number of 1. He lectured extensively and kept alphabetical lists of the cities where he spoke.
- Harary, Frank, Robert Z. Norman, and Dorwin Cartwright, Structural Models: An Introduction to the Theory of Directed Graphs. New York: Wiley, 1965.
- Harary, Frank, Graph Theory (1969), Addison–Wesley, Reading, MA.
- Harary, Frank, and Edgar M. Palmer (1973), Graphical Enumeration. Academic Press, New York, NY.
- Arlinghaus, Sandra Lach, William C. Arlinghaus, and Frank Harary (2002), Graph Theory and Geography: An Interactive E-Book. New York: John Wiley and Sons.
- Hage, Per and Harary, Frank (1991), Exchange in Oceania: A Graph Theoretic Analysis (Oxford Studies in Social and Cultural Anthropology) , Oxford University Press.
- Hage, Per and Harary, Frank (1984), Structural Models in Anthropology (Cambridge Studies in Social and Cultural Anthropology), Cambridge University Press.
- Hage, Per and Harary, Frank (2007), Island Networks: Communication, Kinship, and Classification Structures in Oceania (Structural Analysis in the Social Sciences), Cambridge University Press.
- Harary, Frank (Editor) (1973), New Directions in the Theory of Graphs: Proceedings of the 1971 Ann Arbor Conference on Graph Theory, University of Michigan, Academic Press.
- Buckley, Fred and Harary, Frank (1990), Distance in Graphs, Perseus Press.
- Wilf, Herbert S. and Harary, Frank (Editors) (1971), Mathematical Aspects of Electrical Networks Analysis (Siam-Ams Proceedings, Volume 3), Symposium in Applied Mathematics, American Mathematical Society.
- Harary, Frank (Editor) (1979), Topics in Graph Theory, New York Academy of Sciences.
- Harary, Frank (1967), Graph Theory and Theoretical Physics, Academic Press.
- Frank Harary, a biographical sketch at the ACM SIGACT site
- Frank Harary 1921-2005 - Columbia University
- Alba, Diana M. (2005-01-07). "Late NMSU prof had noted career". Las Cruces Sun-News. p. 1A.
- Harary, F. (1953-54), On the notion of balance of a signed graph. Michigan Math. Journal, vol. 2, pp. 143-146 and addendum preceding p. 1.
- Cartwright, D. and Harary, F. (1956), Structural balance: a generalization of Heider's theory. Psychological Review, vol. 63, pp. 277-293.
- Erdős coauthors