diffusion.degree {centiserve} R Documentation

## 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(lambda(i) * C_D(i), i in neighbors(v))

where C(DD) 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 m_jalili@farabi.tums.ac.ir

### 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)
```

[Package centiserve version 1.0.0 Index]