In this research of network structure analysis, the knowledge of centrality measures is applied to discover or predict a most important actor or node in a network/graph. Problems of energy eciency and sustainability are considered, and also those of allocation of resources. In order to enable an ecient allocation of energy resources to the right path in a distributed network such as obtained in a data center, author ́s network and supply chain network, new measures of centralities are introduced aside from the traditional ones of Closeness, Betweenness, Degree and Eigen-Vector centralities. Mixed-mean centrality, which is based on the generalized degree centrality, was developed as a measure to emphasise the importance of a node in the authorship network and the distributed system of a data centre. Weighted centrality measure when used as against the traditional measures mentioned above was able to make prediction for a Distribution Centre (DC) of a Supply Chain Network with an accuracy of 91.6%. Clique-Structure/Node-weighted centrality measure was able to make a prediction with 66% accuracy, while the Weighted Marking, Clique-Structure/Node-Weighted Centrality made a prediction accuracy of 96.2%. The Top Eigen-Vector Weighted Centrality and Newtonian Gravitational Force were also used to predict the location of distribution centre (DC) in a supply chain network with accuracies of 92.9% and 96.9% respectively.