Information Diffusion and δ-Closeness-Centrality

I consider the issue of optimal targeting in information diffusion networks. The initial information possessor is to target a single node so as to disseminate the infor-mation to all other nodes most effectively. For the purpose, the concept of closeness centrality may be useful, but if the value from delayed information is discounted by a discount factor, the concept should be properly modified. With this respect, I propose a modified concept of point centrality which I will call δ-(closeness)-centrality. The δ-centrality of a node is defined by the sum of discounted values generated from infor-mation transmission starting from the node given discount factor δ. I also provide some alternative scenarios that could justify various measures of closeness-based centrality.