Description Usage Arguments Details Value Author(s) References
View source: R/graph_efficiency.R
This function calculates the global efficiency of a graph or the local or nodal efficiency of each vertex of a graph.
1 2 3 
g 
An 
type 
Character string; either 
weights 
Numeric vector of edge weights; if 
xfm 
Logical indicating whether to transform the edge weights. Default:

xfm.type 
Character string specifying how to transform the weights.
Default: 
use.parallel 
Logical indicating whether or not to use 
A 
Numeric matrix; the adjacency matrix of the input graph. Default:

D 
Numeric matrix; the graph's “distance matrix” 
Local efficiency for vertex i is:
E_{local}(i) = \frac{1}{N} ∑_{i \in G} E_{global}(G_i)
where G_i is the subgraph of neighbors of i, and N is the number of vertices in that subgraph.
Nodal efficiency for vertex i is:
E_{nodal}(i) = \frac{1}{N1} ∑_{j \in G} \frac{1}{d_{ij}}
Global efficiency for graph G with N vertices is:
E_{global}(G) = \frac{1}{N(N1)} ∑_{i \ne j \in G} \frac{1}{d_{ij}}
where d_{ij} is the shortest path length between vertices i and j. Alternatively, global efficiency is equal to the mean of all nodal efficiencies.
A numeric vector of the efficiencies for each vertex of the graph
(if type is localnodal
) or a single number (if type
is global
).
Christopher G. Watson, cgwatson@bu.edu
Latora, V. and Marchiori, M. (2001) Efficient behavior of smallworld networks. Phys Rev Lett, 87.19, 198701. https://dx.doi.org/10.1103/PhysRevLett.87.198701
Latora, V. and Marchiori, M. (2003) Economic smallworld behavior in weighted networks. Eur Phys J B, 32, 249–263. https://dx.doi.org/10.1140/epjb/e2003000955
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