Source-linked AI summary
The energy landscape of social balance
Seth A. Marvel, Steven H. Strogatz, Jon M. Kleinberg
TL;DR
The paper studies local minima in the energy landscape of fully connected signed social networks, where relationships switch to reduce social stress. It defines jammed states, derives energy bounds, constructs arbitrarily large zero-energy examples, and shows that higher-energy states require increasingly complex modular structure.
Problem
Jammed states can trap energy-minimizing dynamics, but their possible energies, structures, and dependence on network size are poorly understood.
Method
The paper defines adjacency by single-edge sign flips, analyzes jammed-state energy bounds, and uses Paley-graph constructions and balanced-clique decompositions.
Results
Jammed states exist arbitrarily close to the midpoint energy for arbitrarily large networks, while approaching U = 0 requires the number of balanced cliques to grow unboundedly with network size.
Takeaways & Limitations
The modular decomposition organizes jammed states and explains why higher-energy states are structurally more complex than lower-energy states.
Takeaways & Limitations
Whether a corresponding construction exists for even m > 6 remains open.
Abstract
from arXiv · showhide
We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others. This notion of social "balance" allows us to define an energy landscape for such networks. Its structure is complex: numerical experiments reveal a landscape dimpled with local minima of widely varying energy levels. We derive rigorous bounds on the energies of these local minima and prove that they have a modular structure that can be used to classify them.