diffusion.degree {centiserve}

Find the variant (Latora) closeness centrality in a disconnected graph

Description

The diffusion degree of a node is defined as the cumulative contribution score of the node itself and its neighbors.

Usage

diffusion.degree(graph, vids = V(graph), mode = c("all", "out", "in"),
  loops = TRUE, lambda = 1)

Arguments

graph

The input graph as igraph object

vids

Vertex sequence, the vertices for which the centrality values are returned. Default is all vertices.

mode

Character constatnt, it specifies how to use the direction of the edges if a directed graph is analyzed. For 'out' only the outgoing edges are followed. For 'in' all vertices from which the source vertex is reachable in at most order steps are counted. 'all' ignores the direction of the edges. This argument is ignored for undirected graphs.

loops

Logical; whether the loop edges are also counted.

lambda

Possibly a numeric vector giving propagation probability of vertices. The default is 1 for all vertices.

Details

Diffusion degree C_{DD} of node v defined as:

C_{DD}(v)=\lambda _{v} * C_{D}(v)+\sum_{i\in neighbors(v)}\lambda _{i} * C_{D}(i)

where C_{D} is degree of of vertex and \lambda is propagation probability of vertex.
In a diffusion process, a node v with propagation probability \lambda _{v}, can activate its neighbor u with probability \lambda _{v}.
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.
More detail at Diffusion Degree

Value

A numeric vector contaning the centrality scores for the selected vertices.

Author(s)

Mahdi Jalili [e-mail]

References

Pal, Sankar K., Suman Kundu, and C. A. Murthy. "Centrality Measures, Upper Bound, and Influence Maximization in Large Scale Directed Social Networks." Fundamenta Informaticae 130.3 (2014): 317-342.

Examples

g <- graph(c(1,2,2,3,3,4,4,2))
diffusion.degree(g)