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: