closeness
Closeness centrality of vertices
Cloness centrality measures how many steps is required to access every other vertex from a given vertex.
- Keywords
- graphs
Usage
closeness(
graph,
vids = V(graph),
mode = c("out", "in", "all", "total"),
weights = NULL,
normalized = FALSE
)estimate_closeness(
graph,
vids = V(graph),
mode = c("out", "in", "all", "total"),
cutoff,
weights = NULL,
normalized = FALSE
)
Arguments
- graph
The graph to analyze.
- vids
The vertices for which closeness will be calculated.
- mode
Character string, defined the types of the paths used for measuring the distance in directed graphs. “in” measures the paths to a vertex, “out” measures paths from a vertex, all uses undirected paths. This argument is ignored for undirected graphs.
- weights
Optional positive weight vector for calculating weighted closeness. If the graph has a
weightedge attribute, then this is used by default. Weights are used for calculating weighted shortest paths, so they are interpreted as distances.- normalized
Logical scalar, whether to calculate the normalized closeness. Normalization is performed by multiplying the raw closeness by \(n-1\), where \(n\) is the number of vertices in the graph.
- cutoff
The maximum path length to consider when calculating the betweenness. If zero or negative then there is no such limit.
Details
The closeness centrality of a vertex is defined by the inverse of the average length of the shortest paths to/from all the other vertices in the graph:
$$\frac{1}{\sum_{i\ne v} d_vi}$$
If there is no (directed) path between vertex \(v\) and \(i\) then the total number of vertices is used in the formula instead of the path length.
estimate_closeness only considers paths of length cutoff or
smaller, this can be run for larger graphs, as the running time is not
quadratic (if cutoff is small). If cutoff is zero or negative
then the function calculates the exact closeness scores.
Value
Numeric vector with the closeness values of all the vertices in
v.
References
Freeman, L.C. (1979). Centrality in Social Networks I: Conceptual Clarification. Social Networks, 1, 215-239.
See Also
Examples
# NOT RUN {
g <- make_ring(10)
g2 <- make_star(10)
closeness(g)
closeness(g2, mode="in")
closeness(g2, mode="out")
closeness(g2, mode="all")
# }