Powerline communications (PLC) has emerged in recent times as a viable compliment to existing wireless communication networks, and it is expected to eventually provide a strong competition to its rivals in the near future. PLC networks consist of numerous segments of branching elements which results in a multiple reflection scenario, a behaviour analogous to that of mobile radio channels. As a result, a multipath modeling approach has found popularity among researchers in capturing the propagation effects in PLC channels. The accuracy of the model is controlled by the number of paths considered in the solution process since there exist theoretically an infinite number of paths between the transmitter and receiver. Thus, the number of dominant or significant paths is critical to the solution process. An unnecessarily large number of paths will result in a solution that is resource intensive with minimal improvement in accuracy, while a relatively smaller choice of number of paths will lead to an inaccurate solution. In this light, an optimum number of paths is required to minimize the resource/accuracy quotient. In this paper, a branched powerline network is considered as a lattice structure and the signal propagation is conveniently represented with a bouncing diagram. The transmission and reflection paths are easily traceable in this representation. Due to possible infinite paths presented to a propagating signal as it travels towards the receiver, an expression that represents only the dominant paths is derived. In this consideration, a restriction is placed on the definition of a 'dominant' path. Since there are no standards governing this assumption, only first order reflections are considered to carry a reasonable amount of energy to have a meaningful contribution towards the total signal level at the receiver. This assumption is one order above the classical two-ray propagation theory applicable to wireless networks. In our derivation, we have considered the possibility of having equal path lengths traversed over different routes. The general model is applicable to a PLC network of any size with a receiver place anywhere in such a network.