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 |

`g` |
An |

`type` |
Character string; either |

`weights` |
Numeric vector of edge weights; if |

`use.parallel` |
Logical indicating whether or not to use |

`A` |
Numeric matrix; the (weighted or unweighted) adjacency matrix of the
input graph (default: |

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}{N-1} ∑_{j \in G} \frac{1}{d_{ij}}*

Global efficiency for graph *G* with *N* vertices is:

*E_{global}(G) = \frac{1}{N(N-1)} ∑_{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 `local|nodal`

) or a single number (if *type*
is `global`

).

Christopher G. Watson, [email protected]

Latora V., Marchiori M. (2001) *Efficient behavior of
small-world networks*. Phys Rev Lett, 87.19:198701.

Latora V., Marchiori M. (2003) *Economic small-world
behavior in weighted networks*. Eur Phys J B, 32:249-263.

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