Compare Two Networks

This function compares two networks using summary metrics, degree distributions, and topological similarity measures. It overlays the complementary cumulative frequency distributions (CCDFs) of degree and returns a combined report.

Usage

compare_networks(
  graph1,
  graph2,
  remove_singles = FALSE,
  show_PL = TRUE,
  PL_exponents = c(2, 3),
  colors = c("#e41a1c", "#000831", "#9c52f2", "#b8b8ff"),
  label.size = 12,
  weights1 = NULL,
  weights2 = NULL,
  weight_type = c("strength", "distance")
)

Arguments

graph1

An igraph object or data.frame (edge list).

graph2

An igraph object or data.frame (edge list).

remove_singles

Logical; remove single nodes before analysis.

show_PL

Logical; whether to fit and display power law exponents.

PL_exponents

Vector; power-law slopes to show.

colors

Optional vector of colors for the CCDF plot.

label.size

Labels' size in the CCDF plot.

weights1, weights2

Optional edge weights for each graph: NULL (default) to ignore them, the name of an edge attribute, or a numeric vector. Supplied separately because the two graphs need not carry the same attribute. See netkit-weights.

weight_type

Either "strength" (default) or "distance", applied to both graphs. See netkit-weights.

Value

A list with:

plot

A ggplot2 object overlaying both CCDF curves.

global_topology

A data frame with one row per input graph, as produced by summarize_graph_metrics().

similarity

A one-row data frame with three distinct set statistics: jaccard_similarity, the Jaccard index of the edge sets (shared edges over their union); node_overlap, the Jaccard index of the vertex sets; and edge_overlap, the overlap coefficient of the edge sets (shared edges over the smaller of the two edge sets). The last is the informative companion to Jaccard when the two networks differ greatly in size – a small network nested inside a large one scores near 1 on overlap and near 0 on Jaccard. Each is NaN where its denominator is empty.

ks_test

The Kolmogorov-Smirnov test comparing the two degree distributions, as returned by stats::ks.test().

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

g1 <- igraph::sample_pa(80, power = 1.5, directed = FALSE)
g2 <- igraph::sample_gnp(80, 0.05, directed = FALSE)
res <- compare_networks(g1, g2)
res$global_topology
#>   Nodes Edges Is_directed Is_weighted    Density Diameter Average_path_length
#> 1    80    79       FALSE       FALSE 0.02500000        7             3.21519
#> 2    80   179       FALSE       FALSE 0.05664557        7             3.09088
#>   Clustering_coefficient Degree_assortativity Avg_degree Avg_strength
#> 1             0.00000000          -0.38504587      1.975        1.975
#> 2             0.07939683           0.02884186      4.475        4.475
#>   Avg_betweenness Components Single_nodes LCC_size LCC_percent
#> 1          87.500          1            0       80      1.0000
#> 2          80.525          2            1       79      0.9875
#>   Algebraic_connectivity Degree_entropy Gini_degree Modularity
#> 1           7.872572e-02       1.399238   0.4359177  0.6154462
#> 2           6.990798e-18       3.052382   0.2655028  0.4223495
res$ks_test
#> 
#> 	Exact two-sample Kolmogorov-Smirnov test
#> 
#> data:  deg1 and deg2
#> D = 0.7, p-value < 2.2e-16
#> alternative hypothesis: two-sided
#>