A Study of Local Sign Change Adjustment in Balancing Structures

Abstract

The adjustment of signed structures (symmetric positive and negative relations) under a local (myopic) sign-change dynamic is studied both analytically and through simulation. Models deriving from various theories but notably balance theory are inspected to determine the convergent properties of the dynamic process.

Keywords:

• signed graphs
• structural balance
• structural dynamics

Notes

¹This article complements a series of earlier papers (Abell and Ludwig, 2009; Abell, Kajawski, and Ludwig, 2009) regarding eventually the location of the simplest micro model which will predict the emergence of groups. Here we concentrate upon structures with symmetric relations under a local sign-change dynamic. Differing assumptions have been made in the other papers. Subsequent papers will explore structures with directed and valued relations. Balance is studied in terms of 3-cycles only as the authors take the view that larger cycles (n > 3) do not lead to stress and are not unstable. In complete structures formulation of balance in terms of 3-cycles and all longer cycles are equivalent. In incomplete structures this is not the case.

² n = 60 is admittedly rather arbitrary, though it was chosen to move beyond a small group context, but in recognition of simulation times.