Computes centrality measures for nodes in a network and returns a tidy data frame. Accepts matrices, igraph objects, cograph_network, or tna objects.
Usage
centrality(
x,
measures = "all",
mode = "all",
normalized = FALSE,
weighted = TRUE,
directed = NULL,
loops = TRUE,
simplify = "sum",
digits = NULL,
sort_by = NULL,
cutoff = -1,
invert_weights = NULL,
alpha = 1,
damping = 0.85,
personalized = NULL,
transitivity_type = "local",
isolates = "nan",
lambda = 1,
k = 3,
states = NULL,
...
)Arguments
- x
Network input (matrix, igraph, network, cograph_network, tna object)
- measures
Which measures to calculate. Default "all" calculates all available measures. Can be a character vector of measure names: "degree", "strength", "betweenness", "closeness", "eigenvector", "pagerank", "authority", "hub", "eccentricity", "coreness", "constraint", "transitivity", "harmonic", "diffusion", "leverage", "kreach", "alpha", "power", "subgraph", "laplacian", "load", "current_flow_closeness", "current_flow_betweenness", "voterank", "percolation".
- mode
For directed networks: "all", "in", or "out". Affects degree, strength, closeness, eccentricity, coreness, and harmonic centrality.
- normalized
Logical. Normalize values to 0-1 range by dividing by max. For closeness, this is passed directly to igraph (proper normalization).
- weighted
Logical. Use edge weights if available. Default TRUE.
- directed
Logical or NULL. If NULL (default), auto-detect from matrix symmetry. Set TRUE to force directed, FALSE to force undirected.
- loops
Logical. If TRUE (default), keep self-loops. Set to FALSE to remove them before calculation.
- simplify
How to combine multiple edges between the same node pair. Options: "sum" (default), "mean", "max", "min", or FALSE/"none" to keep multiple edges.
- digits
Integer or NULL. Round all numeric columns to this many decimal places. Default NULL (no rounding).
- sort_by
Character or NULL. Column name to sort results by (descending order). Default NULL (original node order).
- cutoff
Maximum path length to consider for betweenness and closeness. Default -1 (no limit). Set to a positive value for faster computation on large networks at the cost of accuracy.
- invert_weights
Logical or NULL. For path-based measures (betweenness, closeness, harmonic, eccentricity, kreach), should weights be inverted so that higher weights mean shorter paths? Default NULL which auto-detects: TRUE for tna objects (transition probabilities), FALSE otherwise (matching igraph/sna). Set explicitly to TRUE for strength/frequency weights (qgraph style) or FALSE for distance/cost weights.
- alpha
Numeric. Exponent for weight transformation when
invert_weights = TRUE. Distance is computed as1 / weight^alpha. Default 1. Higher values increase the influence of weight differences on path lengths.- damping
PageRank damping factor. Default 0.85. Must be between 0 and 1.
- personalized
Named numeric vector for personalized PageRank. Default NULL (standard PageRank). Values should sum to 1.
- transitivity_type
Type of transitivity to calculate: "local" (default), "global", "undirected", "localundirected", "barrat" (weighted), or "weighted".
- isolates
How to handle isolate nodes in transitivity calculation: "nan" (default) returns NaN, "zero" returns 0.
- lambda
Diffusion scaling factor for diffusion centrality. Default 1.
- k
Path length parameter for geodesic k-path centrality. Default 3.
- states
Named numeric vector of percolation states (0-1) for percolation centrality. Each value represents how "activated" or "infected" a node is. Default NULL (all nodes get state 1, equivalent to betweenness).
- ...
Additional arguments (currently unused)
Value
A data frame with columns:
node: Node labels/namesOne column per measure, with mode suffix for directional measures (e.g.,
degree_in,closeness_all)
Details
The following centrality measures are available:
- degree
Count of edges (supports mode: in/out/all)
- strength
Weighted degree (supports mode: in/out/all)
- betweenness
Shortest path centrality
- closeness
Inverse distance centrality (supports mode: in/out/all)
- eigenvector
Influence-based centrality
- pagerank
Random walk centrality (supports damping and personalization)
- authority
HITS authority score
- hub
HITS hub score
- eccentricity
Maximum distance to other nodes (supports mode)
- coreness
K-core membership (supports mode: in/out/all)
- constraint
Burt's constraint (structural holes)
- transitivity
Local clustering coefficient (supports multiple types)
- harmonic
Harmonic centrality - handles disconnected graphs better than closeness (supports mode: in/out/all)
- diffusion
Diffusion degree centrality - sum of scaled degrees of node and its neighbors (supports mode: in/out/all, lambda scaling)
- leverage
Leverage centrality - measures influence over neighbors based on relative degree differences (supports mode: in/out/all)
- kreach
Geodesic k-path centrality - count of nodes reachable within distance k (supports mode: in/out/all, k parameter)
- alpha
Alpha/Katz centrality - influence via paths, penalized by distance. Similar to eigenvector but includes exogenous contribution
- power
Bonacich power centrality - measures influence based on connections to other influential nodes
- subgraph
Subgraph centrality - participation in closed loops/walks, weighting shorter loops more heavily
- laplacian
Laplacian centrality using Qi et al. (2012) local formula. Matches NetworkX and centiserve::laplacian()
- load
Load centrality - fraction of all shortest paths through node, similar to betweenness but weights paths by 1/count
- current_flow_closeness
Information centrality - closeness based on electrical current flow (requires connected graph)
- current_flow_betweenness
Random walk betweenness - betweenness based on current flow rather than shortest paths (requires connected graph)
- voterank
VoteRank - identifies influential spreaders via iterative voting mechanism. Returns normalized rank (1 = most influential)
- percolation
Percolation centrality - importance for spreading processes. Uses node states (0-1) to weight paths. When all states equal, equivalent to betweenness. Useful for epidemic/information spreading analysis.
Examples
# Basic usage with matrix
adj <- matrix(c(0, 1, 1, 1, 0, 1, 1, 1, 0), 3, 3)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality(adj)
#> node degree_all strength_all closeness_all eccentricity_all coreness_all
#> 1 A 2 2 0.5 1 2
#> 2 B 2 2 0.5 1 2
#> 3 C 2 2 0.5 1 2
#> harmonic_all diffusion_all leverage_all kreach_all alpha_all power_all
#> 1 2 6 0 2 -1 -1
#> 2 2 6 0 2 -1 -1
#> 3 2 6 0 2 -1 -1
#> betweenness eigenvector pagerank authority hub constraint transitivity
#> 1 0 1 0.3333333 1 1 1.125 1
#> 2 0 1 0.3333333 1 1 1.125 1
#> 3 0 1 0.3333333 1 1 1.125 1
#> subgraph laplacian load current_flow_closeness current_flow_betweenness
#> 1 2.708272 14 5 1.5 0.3333333
#> 2 2.708272 14 5 1.5 0.3333333
#> 3 2.708272 14 5 1.5 0.3333333
#> voterank percolation
#> 1 1.0000000 0
#> 2 0.6666667 0
#> 3 0.3333333 0
# Specific measures
centrality(adj, measures = c("degree", "betweenness"))
#> node degree_all betweenness
#> 1 A 2 0
#> 2 B 2 0
#> 3 C 2 0
# Directed network with normalization
centrality(adj, mode = "in", normalized = TRUE)
#> node degree_in strength_in closeness_in eccentricity_in coreness_in
#> 1 A 1 1 1 1 1
#> 2 B 1 1 1 1 1
#> 3 C 1 1 1 1 1
#> harmonic_in diffusion_in leverage_in kreach_in alpha_in power_in betweenness
#> 1 1 1 0 1 -1 -1 0
#> 2 1 1 0 1 -1 -1 0
#> 3 1 1 0 1 -1 -1 0
#> eigenvector pagerank authority hub constraint transitivity subgraph laplacian
#> 1 1 1 1 1 1 1 1 1
#> 2 1 1 1 1 1 1 1 1
#> 3 1 1 1 1 1 1 1 1
#> load current_flow_closeness current_flow_betweenness voterank percolation
#> 1 1 1 1 1.0000000 0
#> 2 1 1 1 0.6666667 0
#> 3 1 1 1 0.3333333 0
# Sort by pagerank
centrality(adj, sort_by = "pagerank", digits = 3)
#> node degree_all strength_all closeness_all eccentricity_all coreness_all
#> 1 A 2 2 0.5 1 2
#> 2 B 2 2 0.5 1 2
#> 3 C 2 2 0.5 1 2
#> harmonic_all diffusion_all leverage_all kreach_all alpha_all power_all
#> 1 2 6 0 2 -1 -1
#> 2 2 6 0 2 -1 -1
#> 3 2 6 0 2 -1 -1
#> betweenness eigenvector pagerank authority hub constraint transitivity
#> 1 0 1 0.333 1 1 1.125 1
#> 2 0 1 0.333 1 1 1.125 1
#> 3 0 1 0.333 1 1 1.125 1
#> subgraph laplacian load current_flow_closeness current_flow_betweenness
#> 1 2.708 14 5 1.5 0.333
#> 2 2.708 14 5 1.5 0.333
#> 3 2.708 14 5 1.5 0.333
#> voterank percolation
#> 1 1.000 0
#> 2 0.667 0
#> 3 0.333 0
# PageRank with custom damping
centrality(adj, measures = "pagerank", damping = 0.9)
#> node pagerank
#> 1 A 0.3333333
#> 2 B 0.3333333
#> 3 C 0.3333333
# Harmonic centrality (better for disconnected graphs)
centrality(adj, measures = "harmonic")
#> node harmonic_all
#> 1 A 2
#> 2 B 2
#> 3 C 2
# Global transitivity
centrality(adj, measures = "transitivity", transitivity_type = "global")
#> node transitivity
#> 1 A 1
#> 2 B 1
#> 3 C 1