Applications of complex networks-based concepts in hydrology are gaining momentum at the current time. One of the most critical limitations in such studies is the use of linear correlation between the nodes (e.g. rainfall stations) for some assumed threshold levels to identify possible relationships/links. In this regard, entropy theory can be useful to better identify the information flow between the nodes. This study demonstrates the concept of transfer entropy for the directed-weighted complex network to study rainfall dynamics, especially to establish the statistically significant information flow between the nodes. The methodology is applied to a rainfall network of 218 stations across Australia, and total monthly rainfall data observed over the period 1981-2006 are analysed. The nature of the network is studied by determining the in-clustering, out-clustering, and cyclic-clustering coefficients. The highest number of in-clustering values are obtained for the northern parts of Northern Territory and Queensland in addition to the eastern parts of Queensland and New South Wales. Further, the highest number of out-clustering values are also obtained for the northern parts of Northern Territory and Queensland. It can be concluded that while the stations in the northern parts of Australia affect other stations, they are also influenced by others in a reciprocal relationship as shown by the high cyclic-clustering values for these regions. The stations in Western Australia and Victoria have relatively lower in- and out-clustering values, indicating that these stations have lower tendency to make a cluster with other stations. However, while the stations in Western Australia have the lowest clustering coefficients, they have also the highest out-strength values among the stations. These stations constitute a low number of triangles (or groups) with other stations but are significantly influential over other stations, especially located in Victoria (in the southeast). Therefore, the proposed methodology can be useful for determining the tendencies of the nodes in a network to make a cluster with strong or weak relationships with other nodes.