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The dynamics of social relations and the possibility of reaching the state ofstructural balance (Heider balance) are discussed for various networks ofinteracting actors under the influence of the temperature modeling the socialnoise level. For that purpose, two main types of lattices are considered. Thefirst is created by removing some links from a regular triangular lattice toproduce a diluted triangular lattice, and the second by adding more links tocreate an enhanced triangular lattice. In both those cases, the full range ofpossible graph densities is discussed, limited by the extreme cases of networkswhich consist of a small number of separated triads and fully connectednetworks. It is shown that the existence of the balanced state is not possibleif the average node degree is too close to the value characterizing the regulartriangular lattice. Otherwise, both balanced (or partially balanced) andimbalanced states are possible, depending on the temperature. However, only forgraphs which are dense enough a phase transition of the first kind is observed,while less enhanced networks (and all diluted) indicate a smooth cross-overbetween the two states. The cross-over temperatures are size-independent onlyfor the diluted triangular lattices and depend on the size of the system forthe enhanced triangular lattices, as is the case also for the criticaltemperatures of the phase transition observed in denser enhanced lattices.

Thermal properties of structurally balanced systems on diluted and densified triangulations