Pseudo paths towards minimum energy states in network dynamics

The dynamics of networks forming on Heider balance theory moves towards lower tension states. The condition derived from this theory enforces agents to reevaluate and modify their interactions to achieve equilibrium. These possible changes in network's topology can be considered as various paths that guide systems to minimum energy states. Based on this theory the final destination of a system could reside on a local minimum energy, “jammed state”, or the global minimum energy, balanced states. The question we would like to address is whether jammed states just appear by chance? Or there exist some pseudo paths that bound a system towards a jammed state. We introduce an indicator to suspect the location of a jammed state based on the Inverse Participation Ratio method (IPR). We provide a margin before a local minimum where the number of possible paths dramatically drastically decreases. This is a condition that proves adequate for ending up on a jammed states.