حسین رعنایی

To investigate the balance concept in social networks, many models have been introduced. Usually, people and their interactions (friendship or enmity) in a society are considered as nodes and (positive or negative) links of a network, respectively. By considering the triads of relationships as the smallest effective elements in such networks, one seeks to introduce a dynamical model by which an imbalanced state can approach into a balanced final state, in which all triads are balanced and the system is in an stationary balanced state. The outputs of such systems are usually two states: paradise (a society with completely positive relationships) and a bipolar state (a society with two groups of positive internal and negative external relationships). However, there are many examples of multipolar societies in the real world observations. In this thesis, by simulating a society with N elements using a complex network, and by taking into account the famous Ising model in statistical physics, we introduce a model that unlike the previous assumptions, the three-negative interaction triads are considered as balanced. In fact, by introducing a probability p that changes imbalanced triads into balanced ones, we demonstrate that for values of p smaller than p_c, the final state is an N polar society in which the size of every pole is one and for p>pc, the final state is a multipolar society with various pole's sizes. We also observe both types of phase transitions (first and second order), based on the system size N and the level of antipathy in the initial imbalanced societies.