Compare networks across time, layers, or attributes

Performs comprehensive comparison of networks to identify similarities and differences. Supports comparison of edge patterns, structural properties, and node compositions across multiple networks or within subgroups.

Usage

compare_networks(
  nets,
  method = "correlation",
  by = NULL,
  what = "edges",
  test = TRUE,
  n_permutations = 5000,
  include_diagonal = FALSE,
  return_details = FALSE,
  edge_threshold = 0,
  permutation_type = c("classic", "degree_preserving", "freedman_lane", "dsp_mrqap"),
  correlation_type = c("pearson", "spearman"),
  binary_metric = c("phi", "simple_matching", "mean_centered"),
  seed = NULL,
  p_adjust = c("none", "holm", "BH", "BY"),
  adaptive_stop = FALSE,
  alpha = 0.05,
  max_permutations = 20000,
  spectral_rank = 0,
  attr_metric = c("ecdf_cor", "wasserstein")
)

Arguments

nets

Either a list of netify objects to compare, or a single netify object (for longitudinal, multilayer, or by-group comparisons).

method

Character string specifying comparison method:

"correlation": Pearson correlation of edge weights (default)
"jaccard": Jaccard similarity for binary networks
"hamming": Hamming distance (proportion of differing edges)
"qap": Quadratic Assignment Procedure with permutation test
"spectral": Spectral distance based on eigenvalue spectra. Measures global structural differences by comparing the sorted eigenvalues of network Laplacian matrices. Useful for detecting fundamental structural changes.
"all": Applies all applicable methods

by

Character vector of nodal attributes. If specified, compares networks within and between attribute groups rather than across input networks. (Note: Currently not fully implemented)

what

Character string specifying what to compare:

"edges": Edge-level comparison (default)
"structure": Structural properties (density, clustering, etc.)
"nodes": Node composition and attributes
"attributes": Compare networks based on node attribute distributions

test

Logical. Whether to perform significance testing. Default TRUE.

n_permutations

Integer. Number of permutations for QAP test. Default 5000.

include_diagonal

Logical. Whether to include diagonal in comparison. Default FALSE.

return_details

Logical. Whether to return detailed comparison matrices. Default FALSE.

edge_threshold

Numeric or function. For weighted networks, threshold to determine edge presence. Default is 0 (any positive weight).

permutation_type

Character string specifying permutation scheme:

"classic": Standard label permutation QAP (default)
"degree_preserving": Preserves degree sequence (binary networks only)
"freedman_lane": Freeman-Lane MRQAP for controlling autocorrelation
"dsp_mrqap": Double-Semi-Partialling MRQAP

correlation_type

Character string. "pearson" (default) or "spearman" for rank-based correlation.

binary_metric

Character string for binary network correlation:

"phi": Standard phi coefficient (default)
"simple_matching": Proportion of matching edges
"mean_centered": Mean-centered phi coefficient

seed

Integer. Random seed for reproducible permutations. Default NULL.

p_adjust

Character string for multiple testing correction: "none" (default), "holm", "BH" (Benjamini-Hochberg), or "BY".

adaptive_stop

Logical. Whether to use adaptive stopping for permutations. Default FALSE. (Currently not implemented)

alpha

Numeric. Significance level for adaptive stopping. Default 0.05.

max_permutations

Integer. Maximum permutations for adaptive stopping. Default 20000.

spectral_rank

Integer. Number of eigenvalues to use for spectral distance. Default 0 (use all). Set to a smaller value (e.g., 50-100) for large networks to improve performance while maintaining accuracy.

attr_metric

Character string for continuous attribute comparison:

"ecdf_cor": Correlation of empirical CDFs (default)
"wasserstein": Wasserstein-1 (Earth Mover's) distance

Value

A list of class "netify_comparison" containing:

comparison_type: Character string: "cross_network", "temporal", "multilayer", or "by_group"
method: Comparison method(s) used
n_networks: Number of networks compared
summary: Data frame with comparison statistics
edge_changes: List detailing added, removed, and maintained edges (for edge comparisons)
node_changes: List detailing added, removed, and maintained nodes (for node comparisons)
significance_tests: QAP test results if test = TRUE
details: Detailed comparison matrices if return_details = TRUE

Details

The function supports four types of comparisons:

Edge comparison (what = "edges"): Compares edge patterns between networks using correlation, Jaccard similarity, Hamming distance, spectral distance, or QAP permutation tests. Returns detailed edge changes showing which edges are added, removed, or maintained between networks.

Structure comparison (what = "structure"): Compares network-level properties like density, reciprocity, transitivity, and mean degree. For two networks, also provides percent change calculations.

Node comparison (what = "nodes"): Analyzes changes in actor composition between networks, tracking which actors enter or exit the network.

Attribute comparison (what = "attributes"): Compares distributions of node attributes across networks using appropriate statistical tests (KS test for continuous, total variation distance for categorical).

Automatic handling of longitudinal data: When passed a single longitudinal netify object, the function automatically extracts time periods and performs pairwise comparisons between them.

Automatic handling of multilayer networks: When passed a single multilayer netify object (created with layer_netify()), the function automatically extracts layers and performs pairwise comparisons between them. This works for cross-sectional multilayer (3D arrays), longitudinal multilayer (4D arrays), and longitudinal list multilayer formats.

Summary statistics interpretation:

Correlation: Ranges from -1 to 1, measuring linear relationship between edge weights
Jaccard: Ranges from 0 to 1, proportion of edges present in both networks
Hamming: Ranges from 0 to 1, proportion of differing edges
QAP p-value: Significance of observed correlation under random permutation

Permutation methods: When permutation_type = "degree_preserving", the first network must be binary (0/1). This method preserves the degree sequence during permutations, which is important when degree heterogeneity could inflate Type I error rates.

Author

Cassy Dorff, Shahryar Minhas

Examples

# Load example data
data(icews)

# Create networks for different years
net_2002 <- netify(icews[icews$year == 2002, ],
    actor1 = "i", actor2 = "j",
    weight = "matlConf"
)
net_2003 <- netify(icews[icews$year == 2003, ],
    actor1 = "i", actor2 = "j",
    weight = "matlConf"
)

# Basic edge comparison
comp <- compare_networks(list("2002" = net_2002, "2003" = net_2003))
print(comp)
#> 
#> ── Network Comparison Results ──────────────────────────────────────────────────
#> Comparison type: cross_network
#> Number of networks: 2
#> Comparison focus: edges
#> Method: correlation
#> Algorithm: correlation
#> Permutation type: classic
#> Correlation type: pearson
#> Random seed: 1608854729
#> ────────────────────────────────────────────────────────────────────────────────
#> 
#> ── Edge Comparison Summary ──
#> 
#>     comparison correlation
#> 1 2002 vs 2003   0.9431624
#> ── Edge Changes 
#> 2002_vs_2003:
#> Added: 1366 | Removed: 1198 | Maintained: 1866

# Structural comparison
struct_comp <- compare_networks(
    list(net_2002, net_2003),
    what = "structure"
)

# Create longitudinal network for automatic temporal comparison
longit_net <- netify(
    icews,
    actor1 = "i", actor2 = "j",
    time = "year",
    weight = "verbCoop",
    output_format = "longit_list"
)

# Automatic temporal comparison
temporal_comp <- compare_networks(longit_net, method = "all")

# Create multilayer network example
if (FALSE) { # \dontrun{
# Create separate networks for different interaction types
verbal_coop <- netify(
    icews[icews$year == 2010, ],
    actor1 = "i", actor2 = "j",
    weight = "verbCoop"
)

material_coop <- netify(
    icews[icews$year == 2010, ],
    actor1 = "i", actor2 = "j",
    weight = "matlCoop"
)

# Combine into multilayer network
multilayer <- layer_netify(
    list(verbal = verbal_coop, material = material_coop)
)

# Automatic multilayer comparison
layer_comp <- compare_networks(multilayer, method = "all")
print(layer_comp)
# Will show comparison between verbal and material cooperation layers
} # }

# Get detailed matrices
detailed_comp <- compare_networks(
    list(net_2002, net_2003),
    return_details = TRUE
)
names(detailed_comp$details) # Shows available matrices
#> [1] "correlation_matrix" "jaccard_matrix"     "hamming_matrix"    
#> [4] "spectral_matrix"