# Centrality

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** EcologicalNetwork.centrality_katz** —

*Function*.

**Katz's centrality**

centrality_katz(N::Unipartite; a::Float64=0.1, k::Int64=5)

This measure can work on different path length (`k`

), and give a different weight to every subsequent connection (`a`

). `k`

must be at least 1 (only immediate neighbors are considered). `a`

(being a weight), must be positive.

julia> N = UnipartiteNetwork(eye(5)); julia> centrality_katz(N) 5×1 Array{Float64,2}: 0.2 0.2 0.2 0.2 0.2

Katz, L., 1953. A new status index derived from sociometric analysis. Psychometrika 18, 39–43. doi:10.1007/bf02289026

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** EcologicalNetwork.centrality_degree** —

*Function*.

**Degree centrality**

centrality_degree(N::UnipartiteNetwork)

Degree centrality, corrected by the maximum degree (the most central species has a degree of 1).

$C_{d}(i) = k_i / \text{max}(\mathbf{k})$

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** EcologicalNetwork.centrality_closeness** —

*Function*.

**Closeness centrality**

centrality_closeness(N::UnipartiteNetwork; nmax::Int64=100)

Closeness centrality is defined as:

$C_{c}(i) = \sum_j \left( \frac{n-1}{d_{ji}} \right)$

where $mathbf{d}$ is a matrix containing the lengths of the shortest paths between all pairs of species, and $n$ is the number of species.

The function calls `shortest_path`

internally – the `nmax`

argument is the maximal path length that wil be tried.

Bavelas, A., 1950. Communication Patterns in Task‐Oriented Groups. The Journal of the Acoustical Society of America 22, 725–730. doi:10.1121/1.1906679