## Documentation ¶

### Overview ¶

Package network provides network analysis functions.

### Index ¶

- func Betweenness(g graph.Graph) map[int]float64
- func BetweennessWeighted(g WeightedGraph, p path.AllShortest) map[int]float64
- func Closeness(g graph.Graph, p path.AllShortest) map[int]float64
- func Farness(g graph.Graph, p path.AllShortest) map[int]float64
- func HITS(g graph.Directed, tol float64) map[int]HubAuthority
- func Harmonic(g graph.Graph, p path.AllShortest) map[int]float64
- func PageRank(g graph.Directed, damp, tol float64) map[int]float64
- func PageRankSparse(g graph.Directed, damp, tol float64) map[int]float64
- func Residual(g graph.Graph, p path.AllShortest) map[int]float64
- type HubAuthority
- type WeightedGraph

### Constants ¶

This section is empty.

### Variables ¶

This section is empty.

### Functions ¶

#### func Betweenness ¶

Betweenness returns the non-zero betweenness centrality for nodes in the unweighted graph g.

C_B(v) = \sum_{s ≠ v ≠ t ∈ V} (\sigma_{st}(v) / \sigma_{st})

where \sigma_{st} and \sigma_{st}(v) are the number of shortest paths from s to t, and the subset of those paths containing v respectively.

#### func BetweennessWeighted ¶

func BetweennessWeighted(g WeightedGraph, p path.AllShortest) map[int]float64

BetweennessWeighted returns the non-zero betweenness centrality for nodes in the weighted graph g used to construct the given shortest paths.

C_B(v) = \sum_{s ≠ v ≠ t ∈ V} (\sigma_{st}(v) / \sigma_{st})

where \sigma_{st} and \sigma_{st}(v) are the number of shortest paths from s to t, and the subset of those paths containing v respectively.

#### func Closeness ¶

Closeness returns the closeness centrality for nodes in the graph g used to construct the given shortest paths.

C(v) = 1 / \sum_u d(u,v)

For directed graphs the incoming paths are used. Infinite distances are not considered.

#### func Farness ¶

Farness returns the farness for nodes in the graph g used to construct the given shortest paths.

F(v) = \sum_u d(u,v)

For directed graphs the incoming paths are used. Infinite distances are not considered.

#### func HITS ¶

func HITS(g graph.Directed, tol float64) map[int]HubAuthority

HITS returns the Hyperlink-Induced Topic Search hub-authority scores for nodes of the directed graph g. HITS terminates when the 2-norm of the vector difference between iterations is below tol. The returned map is keyed on the graph node IDs.

#### func Harmonic ¶

Harmonic returns the harmonic centrality for nodes in the graph g used to construct the given shortest paths.

H(v)= \sum_{u ≠ v} 1 / d(u,v)

For directed graphs the incoming paths are used. Infinite distances are not considered.

#### func PageRank ¶

PageRank returns the PageRank weights for nodes of the directed graph g using the given damping factor and terminating when the 2-norm of the vector difference between iterations is below tol. The returned map is keyed on the graph node IDs.

#### func PageRankSparse ¶

PageRankSparse returns the PageRank weights for nodes of the sparse directed graph g using the given damping factor and terminating when the 2-norm of the vector difference between iterations is below tol. The returned map is keyed on the graph node IDs.

### Types ¶

#### type HubAuthority ¶

HubAuthority is a Hyperlink-Induced Topic Search hub-authority score pair.