centrality: Calculate Network Centrality Measures

In cograph: Analysis and Visualization of Complex Networks

Calculate Network Centrality Measures

Description

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 as 1 / 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)

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.

Value

A data frame with columns:

• node: Node labels/names

• One column per measure, with mode suffix for directional measures (e.g., degree_in, closeness_all)

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)

# Specific measures
centrality(adj, measures = c("degree", "betweenness"))

# Directed network with normalization
centrality(adj, mode = "in", normalized = TRUE)

# Sort by pagerank
centrality(adj, sort_by = "pagerank", digits = 3)

# PageRank with custom damping
centrality(adj, measures = "pagerank", damping = 0.9)

# Harmonic centrality (better for disconnected graphs)
centrality(adj, measures = "harmonic")

# Global transitivity
centrality(adj, measures = "transitivity", transitivity_type = "global")

cograph documentation built on April 1, 2026, 1:07 a.m.