The degree centrality of node v can be defined as:
where function σ(ui, v) defined as,
σ(u_{i}, v) = 1 if and only if u_{i} and v are connected and = 0 otherwise.
In a diffusion process, a node v with propagation probability λ_{v}, can activate
its neighbor u with probability λ_{v}. So, considerable contribution of node v in
the diffusion process is:
When the diffusion process propagates to the next level, active neighbors of v
will try to activate their inactive neighbors.Thus the cumulative contribution in
the diffusion process by neighbors of v will be maximized when all of its neighbors
will be activated in the previous step. In this scenario, the total contribution of
neighbors of v is:
The diffusion degree of a node is defined as the cumulative contribution score
of the node itself and its neighbors. So, from the above two equations we can define
the diffusion degree C_{DD} of node v as:
Software
References
KUNDU, S., MURTHY, C. A. & PAL, S. K. 2011. A New Centrality Measure for Influence Maximization in Social Networks. In: KUZNETSOV, S., MANDAL, D., KUNDU, M. & PAL, S. (eds.) Pattern Recognition and Machine Intelligence. Springer Berlin Heidelberg.
PAL, S. K., KUNDU, S. & MURTHY, C. 2014. Centrality Measures, Upper Bound, and Influence Maximization in Large Scale Directed Social Networks. Fundamenta Informaticae, 130, 317-342.