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Plot Complementary Cumulative Degree Distribution (CCDF)

Source: R/plot_CCDF.R
plot_CCDF.Rd

This function plots the complementary cumulative distribution function (CCDF) of node degrees in a network and optionally overlays power-law reference curves.

Usage

plot_CCDF(
  graph,
  keep_direction = TRUE,
  remove_singles = FALSE,
  show_PL = TRUE,
  PL_exponents = c(2, 3),
  colors = c("#000831", "#e41a1c", "darkgreen", "#9c52f2", "#b8b8ff"),
  label.size = 12,
  weights = NULL,
  weight_type = c("strength", "distance")
)

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.

keep_direction

Logical. Only for directed graphs. If TRUE, CCDF curves are drawn for 'in'-degree, 'out'-degree, and 'all'-degree distributions. FALSE to ignore directionality.

remove_singles

Logical. If TRUE, nodes with degree 0 are removed from the graph before computing the CCDF. Default is FALSE.

show_PL

Logical. If TRUE, overlays theoretical power-law reference lines of the form \(P(K > k) \sim k^{-\gamma}\). Default is TRUE.

PL_exponents

Numeric vector. The \(\gamma\) exponents for the power-law curves. Default is c(2, 3).

colors

Optional character vector. Custom colors for the graph curve and power-law lines. If NULL, default colors are used.

label.size

Numeric. Font size for axis labels and theme. Passed to theme_minimal.

weights

Optional edge weights: NULL (default) to plot the degree distribution, or the name of an edge attribute / a numeric vector of length igraph::ecount(graph) to plot the vertex strength distribution instead. See netkit-weights.

weight_type

Either "strength" (default) or "distance". See netkit-weights.

Value

A ggplot2 object showing the CCDF of node degrees on a log-log scale.

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.

Examples

g <- igraph::sample_pa(200, power = 1.5, directed = FALSE)
plot_CCDF(g)


# Compare against reference power-law slopes.
plot_CCDF(g, PL_exponents = c(2, 2.5, 3))