A study of sign adjustment in weighted signed networks

We analyse the adjustment of networks comprising of weighted positive (P) and negative (N) symmetric relations under the impact of various balancing rules. Five kinds of rules are studied: (1) a local minimal edge adjustment which is a special case of, (2) a local pressure based rule, (3) a local sign based rule, (4) a global rule and (5) rules varying on a local to global dimension. The convergence and convergent proportions of different 3-cycles and, thus the impact upon β(3) balance, under the different kinds of adjustment rule are studied both analytically and through simulation. The effects of network size (n), density (d) and the initial proportion of positive edges (α0) upon the convergence of 3-cycles and, thus, balance and the eventual implications for the process of group formation are explored.

► We analyse the adjustment of weighted signed networks under four balancing rules.
► We found the assumption that clear groupings will form is far from certain.
► One or two groups emerge under different initial proportion of positive links.
► Patterns observed for binary links are largely conserved.
► More global adjustment makes converge easier.