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Centrality Estimator

PortfolioOptimisers.CentralityEstimator — Type
struct CentralityEstimator{__T_pl, __T_ct} <: AbstractCentralityEstimator

Bundles a network source with the centrality algorithm that scores its assets.

CentralityEstimator encapsulates the configuration for computing centrality measures on a network, including the network estimator and the centrality algorithm.

The network is weighted where it can be. centrality_polarity answers which quantity ct needs — distances for the shortest-path algorithms, similarities for EigenvectorCentrality — and centrality_graph supplies it from pl.

The estimator carries no override of its own. A caller who wants the centrality over the network's topology alone configures ct itself, with TopologyOnly in its ov field, and this estimator is a pure bundle of pl and ct either way.

Warning

Five cases run on the unweighted graph, and none of them raises. A caller names a configured algorithm and never asks for weights, so an unweightable pairing has not been handed a request it cannot serve. TopologyOnly asks away from them, which every source can serve, so it adds no case to this list and is not one of the five.

  1. A clustering estimator or a precomputed Clusters as pl, or a precomputed PhylogenyResult passed to centrality_vector directly. A partition has no edge weights, and does not borrow any.
  2. DegreeCentrality. Graphs.jl ignores weights.
  3. Pagerank. Graphs.jl ignores weights.
  4. KatzCentrality. Graphs.katz_centrality binarises through adjacency_matrix(g, Bool).
  5. EigenvectorCentrality on a tree branch. The branch carries no similarity for it to read.

On the weighted routes the sep field of a NetworkEstimator is inert: they read the structure itself rather than the separation closure phylogeny_matrix builds. At the default HopCount(; n = 1) the two agree, because the closure of a graph at one hop is the graph.

BetweennessCentrality and StressCentrality do read the weights, and are nonetheless unchanged by them on a tree: a tree has exactly one path between any two vertices, so the shortest-path set is the same at any weights. That is a theorem about the graph rather than a limitation of the algorithm, and it does not hold on the similarity branch.

Fields

  • pl: Network estimator, phylogeny result, clustering estimator, or clustering result.
  • ct: Centrality algorithm.

Constructors

CentralityEstimator(;    pl::NwE_ClE = NetworkEstimator(),    ct::AbstractCentralityAlgorithm = DegreeCentrality()) -> CentralityEstimator

Keywords correspond to the struct's fields.

Examples

julia> CentralityEstimator()CentralityEstimator  pl ┼ NetworkEstimator     │    ce ┼ PortfolioOptimisersCovariance     │       │   ce ┼ Covariance     │       │      │    me ┼ SimpleExpectedReturns     │       │      │       │   w ┴ nothing     │       │      │    ce ┼ GeneralCovariance     │       │      │       │   ce ┼ StatsBase.SimpleCovariance: StatsBase.SimpleCovariance(true)     │       │      │       │    w ┴ nothing     │       │      │   alg ┼ FullMoment()     │       │      │     w ┴ nothing     │       │   mp ┼ MatrixProcessing     │       │      │     pdm ┼ Posdef     │       │      │         │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton     │       │      │         │   kwargs ┴ @NamedTuple{}: NamedTuple()     │       │      │      dn ┼ nothing     │       │      │      dt ┼ nothing     │       │      │     alg ┼ nothing     │       │      │   order ┴ NTuple{4, Symbol}: (:pdm, :dn, :dt, :alg)     │    de ┼ Distance     │       │   power ┼ nothing     │       │     alg ┴ CanonicalDistance()     │   alg ┼ KruskalTree     │       │     args ┼ Tuple{}: ()     │       │   kwargs ┴ @NamedTuple{}: NamedTuple()     │   sep ┼ HopCount     │       │   n ┴ Int64: 1  ct ┼ DegreeCentrality     │     kind ┼ Int64: 0     │   kwargs ┴ @NamedTuple{}: NamedTuple()

Related

References

  • [5] D. Cajas. Advanced Portfolio Optimization: A Cutting-edge Quantitative Approach (Springer Nature Switzerland, 2025). Section 13.1.5.1, Equation 13.6.
source

References

[5]
D. Cajas. Advanced Portfolio Optimization: A Cutting-edge Quantitative Approach (Springer Nature Switzerland, 2025).