It has long been investigated and understood that centrality of proteins in the context of protein-protein interaction (PPI) networks are related to their essentiality. In the present work, we validate the relations between essentiality of yeast proteins and their centrality measures in a PPI network by following a different approach using the concept of the receiver operating characteristic (ROC) curve. We found that all centrality measures are related to essentiality. However, the degree centrality performed better in case of the data we used. By deeply examining different centrality values of yeast proteins we find that they are not highly correlated, which has leaded us to hypothesize that centralities might have some relations with gene/protein functions. Indeed, we found that many of the clusters generated based on the pattern of centrality values are rich with similar function proteins. Different types of centrality values imply different types of importance of a node in a network and the functions of genes are of various types. In the present work, we hypothesized that important genes of different functions may tend to show different patterns of centralities and here we show some preliminary links between groups of similar function genes and profiles of centrality values. The concepts of network biology discussed in this paper are applicable to other networks including networks of chemical compounds.