Since seventeenth century that synchronization phenomenon was recognized for the first time, this phenomena have been observed in various branches of natural sciences, engineering and social life. One way to find some synchronized states of a collection of interactive dynamical systems that are modelled by a network is using global symmetris of the network. The advantage of this method is the independence of synchronous patterns from dynamical details of each cell. Certain types of network architecture, with trivial symmetry, still imply the existence of synchronized states. This realization led to a more flexible theory of symmetry, called symmetry groupoid . In asymmetric networks with nontrivial symmetry groupoid, sometimes by defining some special equivalence relation on the network, it is possible to transform it into a smaller symmetric network, called quotient network . Every synchronized states of this quotient network can be lifted to the hy; original asymmetric network. In this thesis after introducing the synchronization phenomenon and the role of symmetry in synchronization of dynamical networks, synchronized states of the smallest nontrivial all to all network (a 3-cell all to all network) is analized. Since this network can be the quotient network of many other larger asymmetric networks, its analyzing is important. So, besides symmetry approach, we have considered its synchrony by numerical method and in FitzHugh-Nagumo model. Because of nonlinearity of this model, analyzing the stability of all patterns of synchrony is not straightforward. Just for one state we succeeded to calculate the stability and the result was the same as the result of the numerical simulation.