Brinkmann graph is a 4-regular graph with 21 nodes and 42 edges discovered by Gunnar Brinkmann in 1992. To our knowledge, the research specifically on Brinkmann graph is still hard to find. Therefore, this research was carried out to analyze the Brinkmann graph in term of its centrality. The centrality measures used are degree, betweenness, and closeness centrality. In this paper, we presented the centrality measures not only on the Brinkmann graph but also on the Brinkmann graph after node deletion to see how the impact of node deletion to the centrality of graph. Before deletion, the results showed that according to the betweenness centrality, there exist 7 nodes who act as mediators or bridges in the Brinkmann graph. Therefore, when a node among these nodes has deleted, it affected not only any other mediator nodes and the furthest nodes from the deleted node but also the nodes that are adjacent to the deleted nodes.