  In social networks, the balance theory has been studied by considering either
the triple interactions between the links (structural balance) or the triple
interaction of nodes and links (coevolutionary balance). In the structural
balance theory, the links are not independent from each other, implying a
global effect of this term and it leads to a discontinuous phase transition in
the system's balanced states as a function of temperature. However, in the
coevolutionary balance the links only connect two local nodes and a continuous
phase transition emerges. In this paper, we consider a combination of both in
order to understand which of these types of interactions will identify the
stability of the network. We are interested to see how adjusting the robustness
of each term versus the other might affect the system to reach a balanced
state. We use statistical mechanics methods and the mean field theory and also
the Monte-Carlo numerical simulations to investigate the behaviour of the order
parameters and the total energy of the system. We find the phase diagram of the
system which demonstrates the competition of these two terms at different
ratios against each other and different temperatures. The system shows a
tricritical point above which the phase transition switches from continuous to
discrete. Also the superiority of the local perspective is observed at low
temperatures and the global view will be the dominant term in determining the
stability of the system at higher temperatures.
