changed or mutated, the change will only be accepted when the local balance index of
triads which formed by this mutating relation have risen. In this case, the mutation of
sentiment relation should not consider the balance of whole triads in network, but only
on the local triads.
From the model, we can investigate the effect of balancing local triads to the
balance of the whole triads in the network. This model is more reliable when we have a
network consists of large number of agents. In this large network, individual agent will
be difficult (if not impossible) to know the whole relations and its balance condition. So
the individual agent only considers his relation with other individual by using the
interpersonal relations in which an agent laid on. Locality principle in this model
represents the bounded rationality caused by limited information of an agent;
information about the balance condition of triads that they have accessed is determined
by their position in the network (Simon, 1955). So, the individual agent will pose based
on local information of the balance condition of his own triads.
After mutation, the new state will be produced. If the mutation raises the local
index balance of triads that formed by the mutating relation, then new state will be
adopted and mutation will continue from this new state. The process will be iterated
until it reaches a balanced configuration that will stay unchanged.
From this point of view, we can obtain the way to investigating how a network
flows in a trajectory to reach balance state and how network configuration formed when
it reaches its balance state.
5. Conclusion
We show how to construct formal procedures and simulations of interpersonal
relationship for many agents based on Heider’s Balance Theory, some adaptation from
Cartwright and Harary (1956) about the structure theorem for graphs and modifications
on Wang & Thorngate (2003). The social balance theory is the theory about balance or
imbalance of sentiment relation in dyadic or triadic relation.
In specific, we propose a new concept to measuring the balance condition of the
sentiment relation network which composed by many agents i.e. the global index
balance which we defined as ratio of the number of balanced triads divided by number
of all possibly formed triads, and the local balance index, defined as the ratio between
the number of balanced triads and the existing number of triads formed by each dyad.
We have investigated how the effect of mutation or change of sentiment relation to the
balance of network.
In the first and simplistic experiment we use the global index as feedback
coefficient where the mutation will be accepted or not by consider the balance condition
of all possible triads in the network. In the next experiment, we complexify the model by
adding locality principle, where mutating relation only consider their local balance
index. In simulation result, we show that the time for the whole network to reach
balance configuration is differ for two models constructed. It is obvious that by the
insight of the algorithmic rule, the first experiment model will be suitable to find the
balance in small group in which the agents are encouraged to know and interact each
other; while the second one, an agent can use other’s interactions as reference on
analyzing her triads.
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