bottleneck {centiserve}

Find the BottleNeck centrality score

Description

BottleNeck Centrality for vertex v defined as:

BN(v) = \sum_{s\in v} P_{s}(v)

Let T_{s} be a shortest path tree rooted at node s. P_{s}(v) = 1 if more than |V(T{s})|/4 paths from node s to other nodes in T_{s} meet at the vertex v, otherwise P_{s}(v) = 0.

Usage

bottleneck(graph, vids = V(graph), mode = c("all", "out", "in"))

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 constant, gives whether the shortest paths to or from the given vertices should be calculated for directed graphs. If out then the shortest paths from the vertex, if in then to it will be considered. If all, the default, then the corresponding undirected graph will be used, ie. not directed paths are searched. This argument is ignored for undirected graphs.

Details

For each node v in the graph, construct a tree T_{v} of shortest paths from that node to all other nodes in the graph. For a node v, n_{v} is the number of nodes that are directly or indirectly connected to node v (i.e. the tree T_{v} contains n_{v} nodes). So extract all nodes w on the above defined tree T_{v} of shortest paths from node v, such that more than n_{v}/4 paths from v to other nodes in the tree meet at node w. Nodes w extracted in this way represent 'bottle necks' of the shortest path tree T_{v} rooted at node v, since at least n_{v}/4 paths of the n_{v}-node tree T_{v} 'meet' at w.
More detail at BottleNeck

Value

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

Author(s)

Mahdi Jalili [e-mail]

References

Przulj, N., Dennis A. Wigle, and Igor Jurisica. "Functional topology in a network of protein interactions." Bioinformatics 20.3 (2004): 340-348.

Examples

g <- graph(c(1,2,2,3,3,4,4,2))
bottleneck(g)