# Frank Harary

## Balance theory

Signed graphs http://emis.impa.br/EMIS/journals/EJC/Surveys/ds8.ps

Harary, Frank, Kabell, Jerald A. (1980/09)."A simple algorithm to detect balance in signed graphs." Mathematical Social Sciences 1(1): 131-136. <http://hdl.handle.net/2027.42/23150> http://deepblue.lib.umich.edu/bitstream/2027.42/23150/1/0000075.pdf

- Cobalance means that every cutset has positive sign product. Thm: Σ is cobalanced iff every vertex star has evenly many negative edges. [The theorem follows easily by looking at the negative subgraph].

Peter Abell and Mark Ludwig. 2009. Structural Balance: A Dynamic Perspective. Journal of Mathematical Sociology.

Peter Abell. 1968. [ Structural Balance in Dynamic Structures]. Sociology 2: 333-352.

## Networks

Harary, Frank, and M. F. Batell. 1981. What is a system? Social Networks 3(1): 29-40.

Harary, Frank, and Douglas R. White. 1997. P-Systems: a structural model for kinship studies. Connections 24(2):22-33.

Douglas R. White & Frank Harary. 2001. The Cohesiveness of Blocks in Social Networks: Node Connectivity and Conditional Density. (31):305-359. download:PDF - Sociological Methodology 2001, eds. Mark Sobel and Mark Becker. American Sociological Association. Blackwell Publications.

Harary proposal - e.g., for Ernesto Estrada's method