core: Core-periphery clustering algorithms

In migraph: Multimodal Network Analysis and More

Core-periphery clustering algorithms

Description

This function is used to identify which nodes should belong to the core, and which to the periphery. It seeks to minimize the following quantity:

Z(S_1) = \sum_{(i<j)\in S_1} \textbf{I}_{\{A_{ij}=0\}} + \sum_{(i<j)\notin S_1} \textbf{I}_{\{A_{ij}=1\}}

where nodes \{i,j,...,n\} are ordered in descending degree, A is the adjacency matrix, and the indicator function is 1 if the predicate is true or 0 otherwise. Note that minimising this quantity maximises density in the core block and minimises density in the periphery block; it ignores ties between these blocks.

Usage

node_core(.data, method = c("degree", "eigenvector"))

node_coreness(.data)

Arguments

.data	An object of a {manynet}-consistent class: matrix (adjacency or incidence) from {base} R edgelist, a data frame from {base} R or tibble from {tibble} igraph, from the {igraph} package network, from the {network} package tbl_graph, from the {tidygraph} package
method	Which method to use to identify cores and periphery. By default this is "degree", which relies on the heuristic that high degree nodes are more likely to be in the core. An alternative is "eigenvector", which instead begins with high eigenvector nodes. Other methods, such as a genetic algorithm, CONCOR, and Rombach-Porter, can be added if there is interest.

Functions

• node_coreness(): Returns k-cores

References

Borgatti, Stephen P., & Everett, Martin G. 1999. Models of core /periphery structures. Social Networks, 21, 375–395. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0378-8733(99)00019-2")}

Lip, Sean Z. W. 2011. “A Fast Algorithm for the Discrete Core/Periphery Bipartitioning Problem.” \Sexpr[results=rd]{tools:::Rd_expr_doi("10.48550/arXiv.1102.5511")}

See Also

Other memberships: community, components(), equivalence

Examples

#mpn_elite_usa_advice %>% as_tidygraph %>% 
#   mutate(corep = node_core(mpn_elite_usa_advice)) %>% 
#   autographr(node_color = "corep")
network_core(mpn_elite_usa_advice)
node_coreness(ison_adolescents)

migraph documentation built on Nov. 2, 2023, 5:47 p.m.