Identifying influential nodes in complex networks is a very challenging task in network science with paramount importance. It has many applications, including preventing and controlling rumours in social networks, preventing contagious disease spread, political and marketing campaigns. Solutions to this problem typically rely on the ranking of individual nodes based on some centrality measures. It is assumed that nodes having higher centrality values are more influential. Influence maximization (IM) is another form of this problem, where a set of influential nodes (seed nodes) are selected that maximizes the total influence spread in the network. Popular centrality measures like degree, betweenness centrality, closeness centrality, PageRank are also used to select top-ranked nodes as seed nodes, but this type of approach suffers from the overlapping of influences between the selected seed nodes. In this work, we propose a new type of centrality measure called penalty based on neighbour’s degree, i.e., PND that uses a penalty mechanism to calculate the centrality values. A node is penalized by each of its neighbours. The penalty amount is determined by the degree of the node and the degree of its neighbour. The total penalty paid by a node determines its influencing capability. Although the proposed approach is designed to address the issue of overlapping influence in the influence maximization (IM) problem, experimental results demonstrate its effectiveness not only for the IM problem but also for ranking individual nodes.