Graph Centrality

katz(g, alpha = 0.1)

Compute the Katz centrality for a static graph g.

References:

1. L. Katz A new index derived from sociometric data analysis. Psychometrika, 18:39-43, 1953.

katz(g, alpha = 0.3)
katz(g, alpha, beta; mode = :broadcast)

Computes the katz centrality for an evolving graph g, where alpha and beta are scalars. alpha controls the influence of long walks and beta controls the influence of walks happened long time ago. By default, mode = :broadcast computes the broadcast centrality. Otherwise if mode = :receive, we compute the receiving centrality.

Example

julia> using EvolvingGraphs

julia> using EvolvingGraphs.Centrality

julia> g = evolving_graph_from_arrays(["A", "B", "B", "C", "E", "A", "B", "D"], ["B", "F", "G", "E", "G", "B", "F", "F"], [1,1,1,2,2,2,2,2])
Directed EvolvingGraph 7 nodes, 8 static edges, 2 timestamps

julia> katz(g)
7-element Array{Tuple{EvolvingGraphs.Node{String},Float64},1}:
 (Node(A), 0.510104)
 (Node(B), 0.494488)
 (Node(F), 0.260257)
 (Node(G), 0.260257)
 (Node(C), 0.361757)
 (Node(E), 0.338334)
 (Node(D), 0.338334)

julia> katz(g, 0.3, 0.4, mode = :receive)
7-element Array{Tuple{EvolvingGraphs.Node{String},Float64},1}:
 (Node(A), 0.0)
 (Node(B), 0.658926)
 (Node(F), 1.0)
 (Node(G), 0.658926)
 (Node(C), 0.0)
 (Node(E), 0.204852)
 (Node(D), 0.0)

References:

1. P. Grindrod, D. J. Higham, M. C. Parsons and E. Estrada Communicability across evolving networks. Physical Review E, 83 2011.

2. P. Grindrod and D. J. Higham, A matrix iteration for dynamic network summaries. SIAM Review, 55 2013.