Compute a Table of Node-Level Centrality Metrics

Computes several per-node centrality and position metrics in one call and returns them as a tibble, with every metric also attached to the graph as a vertex attribute.

Usage

node_metrics(
  graph,
  metrics = c("degree", "strength", "betweenness", "harmonic", "eigenvector", "pagerank",
    "coreness", "clustering", "constraint", "eccentricity"),
  weights = NULL,
  weight_type = c("strength", "distance"),
  normalized = TRUE,
  mode = c("all", "in", "out"),
  max_nodes = 5000,
  plot = TRUE,
  plot_type = c("correlation", "ranking"),
  top_n = 15,
  label.size = 12
)

Arguments

graph: An igraph object representing the network to analyze, or a data frame containing a symbolic edge list in the first two columns. Additional columns are considered as edge attributes.
metrics: Character vector of metrics to compute. Any subset of "degree", "strength", "betweenness", "closeness", "harmonic", "eigenvector", "pagerank", "coreness", "clustering", "constraint" and "eccentricity". Defaults to all but "closeness" – see Details.
weights: Optional edge weights: NULL (default) to ignore them, the name of an edge attribute, or a numeric vector of length igraph::ecount(graph). See netkit-weights.
weight_type: Either "strength" (default) or "distance". See netkit-weights.
normalized: Logical. If TRUE (default), metrics that igraph can normalize to [0, 1] are normalized, which makes them comparable across graphs of different size.
mode: For directed graphs, whether to count "all" (default), "in" or "out" edges. Ignored for undirected graphs.
max_nodes: Integer. Above this vertex count, the metrics whose cost is O(VE) – "betweenness", "closeness", "harmonic" and "eccentricity" – are skipped with a warning and returned as NA. Set to Inf to compute them regardless. Default is 5000, matching the threshold summarize_graph_metrics() already uses for betweenness.
plot: Logical. Whether to build a diagnostic plot. Default is TRUE.
plot_type: Either "correlation" (default), a Spearman correlation heatmap of the computed metrics, or "ranking", a faceted bar chart of the top_n highest-scoring nodes per metric.
top_n: Integer. Number of nodes shown per facet when plot_type = "ranking". Default is 15.
label.size: Numeric. Base font size for plot text. Default is 12.

Value

A list with:

plot: A ggplot2 object, or NULL when plot = FALSE. The element is always present, so the return shape does not depend on the arguments.
result: A tibble with one row per vertex: node followed by one column per requested metric, in the order given by metrics.
graph: The input graph with each metric attached as a vertex attribute of the same name.
method: A human-readable description of what was computed.

Details

This is the node-level counterpart to summarize_graph_metrics(), which describes the graph as a whole. Having both means a ranking of nodes no longer has to be stitched together from individual igraph calls, and because the returned graph carries the metrics as vertex attributes, the result feeds directly into plot_Net() (color = "pagerank") and into robustness_analysis() (removal_strategy = "pagerank"), which already accepts any numeric vertex attribute as a removal priority.

The metrics are:

degree: Number of incident edges. Always the unweighted count.
strength: Sum of incident edge weights; equal to degree when unweighted.
betweenness: Fraction of shortest paths passing through the node. Uses edge costs when weighted.
closeness: Reciprocal of the mean distance to all reachable nodes. Not comparable across components – see below.
harmonic: Sum of the reciprocal distances. Unlike closeness this is comparable across components, because an unreachable pair contributes \(1/\infty = 0\) rather than being excluded from the average.
eigenvector: Leading eigenvector of the adjacency matrix: a node is central if its neighbors are.
pagerank: Stationary distribution of a random surfer. Sums to 1.
coreness: Largest k for which the node belongs to the k-core.
clustering: Local transitivity: how interconnected the node's neighborhood is. NaN for nodes of degree below 2, which have no neighbor pairs.
constraint: Burt's constraint: how much the node's connections are concentrated within a single group. Low constraint marks a broker.
eccentricity: Distance to the furthest reachable node.

"closeness" is omitted from the defaults because it is not comparable across components, and most real networks are disconnected. igraph averages the distance over reachable vertices only, so a node in a small isolated component scores higher than an equally well-placed node in the giant component – everything in its component is nearby. Ranking by closeness on a fragmented graph therefore puts the periphery on top. "harmonic" answers the same question without that failure mode, because unreachable pairs contribute zero rather than being dropped from the denominator. Request "closeness" explicitly if the graph is connected or you want the per-component reading.

The default plot is a correlation heatmap rather than a ranking because the most common mistake with a table like this is to treat the metrics as independent evidence. On many networks betweenness, eigenvector centrality and PageRank correlate with degree above 0.9, so a node that looks important by four measures may be important by one. The heatmap makes that visible before the ranking is interpreted.

Edge weights

Functions that can use edge weights take two arguments:

weights: NULL (the default) to ignore edge weights; the name of an edge attribute, such as "weight"; or a numeric vector with one value per edge, in igraph::E(graph) order.
weight_type: "strength" (the default) if a larger value means a more tightly connected pair – confidence scores, correlations, co-expression, read counts, interaction scores. "distance" if a larger value means further apart – costs, dissimilarities, reaction times.

Declaring which you have is not bookkeeping. igraph reads the weight attribute implicitly and gives it opposite meanings in different functions: a cost in igraph::betweenness(), igraph::distances(), igraph::diameter() and igraph::mean_distance(), but a strength in igraph::cluster_louvain() and the other community detection algorithms. Attaching a confidence score and letting that happen implicitly therefore inverts every path-based metric – a high-confidence interaction is treated as a long distance – while community detection reads the same numbers the way you intended.

netkit resolves weights and weight_type once per call and derives both a strength and a distance vector from them, so each metric receives the one it needs. A "strength" is converted to a distance by reciprocal (\(1/w\)); a "distance" is converted to a strength by reflection (\(\max(w) - w + \min(w)\)), which keeps a zero distance finite.

References

Freeman, L. C. (1978). Centrality in social networks: conceptual clarification. Social Networks, 1(3), 215-239. doi:10.1016/0378-8733(78)90021-7

Burt, R. S. (1992). Structural Holes: The Social Structure of Competition. Harvard University Press.

Marchiori, M., & Latora, V. (2000). Harmony in the small-world. Physica A, 285(3-4), 539-546. doi:10.1016/S0378-4371(00)00311-3

Examples

g <- igraph::sample_pa(60, power = 1.5, directed = FALSE)
igraph::V(g)$name <- paste0("n", seq_len(igraph::vcount(g)))

res <- node_metrics(g, plot = FALSE)
head(res$result)
#> # A tibble: 6 × 11
#>   node  degree strength betweenness harmonic eigenvector pagerank coreness
#>   <chr>  <dbl>    <dbl>       <dbl>    <dbl>       <dbl>    <dbl>    <dbl>
#> 1 n1    0.186        11      0.510     0.450      0.239   0.0839         1
#> 2 n2    0.0169        1      0         0.296      0.0575  0.00898        1
#> 3 n3    0.102         6      0.571     0.451      0.391   0.0453         1
#> 4 n4    0.271        16      0.729     0.522      1       0.122          1
#> 5 n5    0.0339        2      0.0339    0.338      0.255   0.0174         1
#> 6 n6    0.0169        1      0         0.327      0.240   0.00896        1
#> # ℹ 3 more variables: clustering <dbl>, constraint <dbl>, eccentricity <dbl>

# Every metric is on the returned graph, so it chains straight onward.
igraph::vertex_attr_names(res$graph)
#>  [1] "name"         "degree"       "strength"     "betweenness"  "harmonic"    
#>  [6] "eigenvector"  "pagerank"     "coreness"     "clustering"   "constraint"  
#> [11] "eccentricity"
rob <- robustness_analysis(res$graph, removal_strategy = "pagerank",
                           steps = 10, plot = FALSE)
rob$auc$lcc_size
#> [1] 0.08637549

# The default plot shows how far the metrics actually disagree.
p <- node_metrics(g, metrics = c("degree", "betweenness", "pagerank"))$plot