DrugClaw: Structural Characterization of Pharmacological Interaction Networks

Introduction

Pharmacological interaction networks (drug-drug, drug-target, disease-disease, protein-protein) encode the relational structure of biomedical systems, yet their graph-theoretic properties are rarely compared systematically across interaction types. Understanding whether different pharmacological network categories exhibit distinct topological signatures has practical value for link prediction, drug repurposing pipelines, and network-based toxicology screening, where structural assumptions (e.g., scale-free degree distributions, high clustering) are often imported from one domain and applied to another without verification.

This work provides an exploratory structural characterization of $n = 8$ pharmacological and social-baseline networks drawn from BioSNAP and SNAP, spanning $5$ interaction domains: drug-drug interactions, drug-gene targets, disease-disease associations, protein-protein interactions, and social networks (included as a non-pharmacological baseline). With $n = 8$, this work is exploratory. We characterize observable patterns without claiming statistical generalization. Each network is described by $15$ topological metrics (plus $3$ size-normalized variants), tested for cross-domain differences via the Kruskal-Wallis rank-sum test with Bonferroni and Benjamini-Hochberg corrections, and classified by domain using a Random Forest leave-one-out cross-validation protocol.

The asymptotic relative efficiency (ARE) of the Mann-Whitney U test relative to the $t$-test is $3/\pi \approx 0.955$ on normal data (Hodges and Lehmann, 1956), meaning rank-based tests sacrifice only about $4.5$ efficiency in the best case for parametric tests. On non-normal data the ARE can exceed $1.0$, making non-parametric tests more efficient. Given the small sample sizes and unknown distributional forms in this study, we use the Kruskal-Wallis test (the $k$-sample generalization of the Mann-Whitney U test) throughout, accepting a minor efficiency cost under normality in exchange for validity under arbitrary distributions.

The remainder of the paper is organized as follows: Methods describes data collection, metric computation, statistical testing, classification, and reproducibility controls. Results presents metric distributions, hypothesis test outcomes, multiple-testing corrections, size-confounding analysis, and classification performance. Discussion interprets the findings and connects them to the exploratory framing. Limitations lists specific constraints on generalizability. Conclusion summarizes the contribution.

Methods

Data Collection

Eight networks were downloaded from two Stanford repositories using Python's urllib.request module (Python 3.11). Five pharmacological networks came from BioSNAP (https://snap.stanford.edu/biodata/):

Three social-baseline networks came from SNAP (https://snap.stanford.edu/data/):

BioSNAP files were downloaded as compressed CSV/TSV archives, decompressed with gzip, and parsed to tab-separated edge lists. SNAP files were downloaded as .txt.gz archives and decompressed directly. SHA-256 checksums were computed for each raw file at download time to verify data integrity. No filtering or edge removal was applied; all edges in the original files were retained. Network sizes range from $1{,}510$ nodes and $6{,}877$ edges (DD-Miner) to $33{,}696$ nodes and $715{,}602$ edges (PP-Decagon).

The configuration originally specified $10$ networks ($7$ BioSNAP pharmacological networks plus $3$ SNAP baselines). Two BioSNAP networks (ChSe-Miner side-effect and FF-Miner functional) did not produce valid results, leaving $8$ networks in the final analysis.

Feature Extraction

For each network, $15$ topological metrics were computed using NetworkX 3.4.2, plus $3$ size-normalized variants ($18$ total):

Scale-dependent metrics: num_nodes, num_edges, density, avg_degree, max_degree, avg_clustering, transitivity, avg_shortest_path_sample, diameter_sample, assortativity, num_components, largest_component_fraction.

Derived metrics: powerlaw_alpha and powerlaw_xmin (fitted via the powerlaw 1.5 package using the Clauset-Shalizi-Newman method), and modularity (Louvain community detection via python-louvain 0.16 with random_state=42).

Size-normalized variants: max_degree_norm (max_degree / num_nodes), avg_degree_norm (avg_degree / num_nodes, equivalent to density), and diameter_norm (diameter / sqrt(num_nodes)).

Shortest path length and diameter were computed on a random sample of $500$ source nodes (or all nodes if fewer than $500$) to keep computation tractable on larger networks. All stochastic operations used random_state=42 or np.random.seed(42).

Two metrics (num_components and largest_component_fraction) were constant across all $8$ networks (every network was a single connected component with fraction $1.0$) and were excluded from statistical testing.

Statistical Testing

The Kruskal-Wallis $H$ test (scipy.stats.kruskal, SciPy 1.15.2) was applied independently to each of the $16$ non-constant metrics, testing the null hypothesis that the metric distributions are identical across the $5$ domains. The Kruskal-Wallis test was chosen because (a) group sizes are extremely small ($1$ to $3$ networks per domain), precluding parametric assumptions, and (b) the test is valid for ordinal data and makes no distributional assumptions beyond continuous distributions within groups.

Because $16$ simultaneous hypothesis tests inflate the family-wise error rate, two multiple-comparison corrections were applied:

1. Bonferroni correction: $\alpha_{\text{adj}} = 0.05 / 16 = 0.003125$. Each uncorrected $p$-value was multiplied by $16$ and capped at $1.0$.
2. Benjamini-Hochberg FDR correction: Applied via scipy.stats.false_discovery_control with method='bh' at $q < 0.05$.

Both corrections were computed in the upstream statistical analysis code and stored in the results JSON, not computed post hoc.

Classification

A Random Forest classifier (sklearn.ensemble.RandomForestClassifier, scikit-learn 1.6.1, n_estimators=100, random_state=42) was trained on all $15$ base metrics to predict the domain label of each network. Leave-one-out cross-validation (LOO-CV) was used because $n = 8$ is too small for $k$-fold stratified splits to produce meaningful held-out sets.

A stratified random baseline was established using sklearn.dummy.DummyClassifier(strategy='stratified', random_state=42) under the same LOO-CV protocol. This baseline reflects the accuracy expected from random guessing that respects class proportions.

Gini feature importances were extracted from the full-data model to identify the most discriminative metrics. A UMAP embedding (umap-learn 0.5.7, n_neighbors=3, min_dist=0.1, random_state=42) was computed from the $15$-metric feature matrix to visualize network separation in two dimensions.

Reproducibility

All random seeds were set to $42$ (numpy, random module, scikit-learn random_state, UMAP random_state, Louvain random_state). Computation used n_jobs=1 throughout to avoid non-deterministic thread scheduling. All figure DPI was fixed at $150$. The analysis ran inside a python:3.11-slim Docker container with pinned dependencies in requirements.txt:

• networkx==3.4.2, python-louvain==0.16, scikit-learn==1.6.1
• scipy==1.15.2, pandas==2.2.3, numpy==2.2.3
• matplotlib==3.10.1, seaborn==0.13.2, umap-learn==0.5.7, powerlaw==1.5

SHA-256 checksums of downloaded data files were logged at download time. All results are deterministic and fully reproducible given the same Docker image and pinned requirements.

Results

Network Metric Profiles

The $8$ networks span a wide range of structural properties. Node counts range from $1{,}510$ (ChCh-Miner, drug interaction) to $33{,}696$ (email-Enron, social baseline). Edge counts range from $6{,}877$ (DD-Miner, disease interaction) to $715{,}602$ (PP-Decagon, protein interaction). Density ranges from $0.000291$ (DD-Miner) to $0.0426$ (ChCh-Miner). All $8$ networks consist of a single connected component (largest_component_fraction $= 1.0$).

Table 1 presents the full metric profile for all $8$ networks.

Table 1. Structural metrics for $8$ pharmacological and baseline networks.

Observable patterns include: the social baseline networks exhibit the highest average clustering coefficients (mean $0.557$), while the drug-target (ChG-Miner) and disease-interaction (DD-Miner) networks have zero clustering. The disease-interaction network (DD-Miner) has the highest modularity ($0.974$), consistent with a sparse, tree-like structure (avg_degree $= 2.00$). Protein-interaction networks have the highest edge counts and average degrees, while drug-target and disease-interaction networks are the sparsest.

Kruskal-Wallis Tests Across Domains

Kruskal-Wallis tests were conducted on $16$ non-constant metrics across the $5$ domains. No metric reached significance at $\alpha = 0.05$ (uncorrected). The smallest uncorrected $p$-value was $p = 0.0679$ for diameter_sample ($H = 3.33$). Seven metrics had $p = 0.0833$ (num_edges, max_degree, avg_clustering, avg_shortest_path_sample, powerlaw_xmin, modularity, diameter_norm, all with $H = 3.0$). The remaining metrics had $p > 0.24$.

Table 2. Kruskal-Wallis test results for the $5$ lowest $p$-value metrics.

Multiple Testing Correction

Before correction, $0$ of $16$ metrics showed $p < 0.05$. After Bonferroni correction at $\alpha_{\text{adj}} = 0.05/16 = 0.003125$, $0$ metrics were significant. After Benjamini-Hochberg FDR correction at $q < 0.05$, $0$ metrics were significant (smallest adjusted $q = 0.167$). The complete absence of significant differences, even before correction, indicates that the observed variation across domains is within the range expected under the null hypothesis given the very small group sizes ($1$ to $3$ networks per domain).

Size Confounding Analysis

Because the $8$ networks span a wide range of sizes ($1{,}510$ to $33{,}696$ nodes), Spearman rank correlations between num_nodes and each of the $15$ non-constant metrics were computed to assess size confounding. A metric was flagged as size-confounded if $|\rho| > 0.5$ and $p < 0.05$.

No metric met both criteria simultaneously. The strongest correlations were density ($\rho = -0.667$, $p = 0.071$) and avg_degree_norm ($\rho = -0.667$, $p = 0.071$), both approaching but not reaching significance at $\alpha = 0.05$. The metric max_degree had $\rho = 0.595$ ($p = 0.120$) and powerlaw_alpha had $\rho = -0.548$ ($p = 0.160$). With $n = 8$ observations, the power to detect size confounding is limited, and several metrics show moderate correlations ($|\rho| > 0.5$) that would likely reach significance with a larger sample.

Table 3. Metrics with $|\rho| > 0.4$ for Spearman correlation with num_nodes.

Classification Performance

Random Forest LOO-CV accuracy was $62.5$ ($5$ of $8$ networks classified correctly) versus a stratified random baseline of $0.0$ ($0$ of $8$). The Random Forest improvement over baseline is $62.5$ percentage points. With $n = 8$ and $5$ classes, this result is descriptive of separability, not predictive of generalization. The Wilson $95$ confidence interval for the observed proportion $\hat{p} = 0.625$ at $n = 8$ is approximately $(0.29, 0.88)$, which is wide and includes the theoretical random expectation of $0.20$ (for $5$ equiprobable classes), though the actual class distribution is imbalanced.

Figure 1 (figures/confusion_heatmap.png) shows the confusion matrix. All $3$ social_baseline networks were classified correctly. Both protein_interaction networks were classified correctly. The $3$ singleton-domain networks (ChCh-Miner drug_interaction, ChG-Miner drug_target, DD-Miner disease_interaction) were all misclassified: ChCh-Miner was predicted as protein_interaction, ChG-Miner as disease_interaction, and DD-Miner as drug_target. This pattern is expected: domains with only $1$ training example provide no within-domain variance for the classifier to learn from in LOO-CV (the single example is the held-out test sample, leaving zero training examples for that class).

The top-$5$ discriminative metrics by Gini importance were: avg_clustering ($0.131$), powerlaw_xmin ($0.109$), modularity ($0.094$), powerlaw_alpha ($0.091$), and max_degree ($0.086$). Figure 2 (figures/feature_importance.png) shows the full importance ranking. Figure 3 (figures/domain_boxplots.png) shows boxplots of these top-$5$ metrics by domain, illustrating how social_baseline networks cluster at high avg_clustering ($> 0.5$) while pharmacological networks are more heterogeneous.

Figure 4 (figures/domain_embedding_umap.png) shows the UMAP 2D embedding of the $15$-metric feature vectors, colored by domain. The $3$ social_baseline networks do not form a tight cluster (email-Enron is distant from ca-GrQc and ego-Facebook), and the $2$ protein_interaction networks (PP-Decagon and PP-Pathways) are adjacent. The pharmacological singleton networks are scattered without clear domain grouping, consistent with the null statistical test results.

All results are deterministic and fully reproducible given the pinned Docker image and fixed random seeds.

Discussion

The central finding of this exploratory analysis is negative: no topological metric differs significantly across the $5$ pharmacological and baseline network domains, even before multiple-testing correction. This null result is consistent with (a) the very small sample size ($n = 8$ total, with $3$ domains having only $1$ network each), which severely limits the power of the Kruskal-Wallis test, and (b) genuine structural overlap between pharmacological and social network topologies at the resolution of standard graph metrics.

Despite the null hypothesis test results, the Random Forest classifier achieved $62.5$ LOO-CV accuracy, compared to $0$ for a stratified random baseline. This suggests that the $15$-metric feature space does contain some discriminative signal, even if individual metrics do not reach significance in univariate tests. The classifier's success was concentrated in domains with multiple representatives (social_baseline: $3/3$ correct, protein_interaction: $2/2$ correct), while singleton domains were uniformly misclassified. This is a direct consequence of the LOO-CV protocol: removing the single example of a domain leaves zero training examples for that class.

The most discriminative metric, avg_clustering ($\text{importance} = 0.131$), separates social_baseline networks (mean $0.557$) from the tree-like disease_interaction network ($0.0$) and the drug-target network ($0.0$). However, protein_interaction networks (mean $0.181$) and the drug_interaction network ($0.305$) occupy an intermediate range, preventing clean separation. The Kruskal-Wallis test for avg_clustering ($H = 3.0$, $p = 0.083$) approached but did not reach significance, consistent with the ARE prediction that rank-based tests sacrifice approximately $4.5$ efficiency relative to parametric alternatives on normal data. On the non-normal distributions observed here (several metrics have zero values or extreme outliers), the non-parametric approach likely performs at or above its ARE-predicted efficiency.

The size-confounding analysis found no metric meeting the joint criterion of $|\rho| > 0.5$ and $p < 0.05$ for Spearman correlation with num_nodes. However, several metrics (density, max_degree, powerlaw_alpha, transitivity) showed moderate correlations ($|\rho|$ between $0.5$ and $0.7$) that failed to reach significance only because of the small sample size. This does not rule out size confounding; it indicates insufficient power to detect it.

The absence of significant cross-domain differences should not be interpreted as evidence that pharmacological networks are structurally interchangeable. The sample is too small to draw such a conclusion. Rather, this analysis provides an exploratory profile of $8$ specific networks that can inform future, larger-scale comparisons.

Limitations

1. Extremely small sample size. The analysis includes only $n = 8$ networks across $5$ domains, with $3$ domains represented by a single network each. This severely limits statistical power for hypothesis testing and means classification results for singleton domains are undefined under LOO-CV. All findings should be interpreted as exploratory, not confirmatory.

2. No metric reached significance, even uncorrected. The smallest uncorrected $p$-value was $0.0679$. After Bonferroni correction ($\alpha_{\text{adj}} = 0.003125$) and Benjamini-Hochberg FDR correction ($q < 0.05$), all $16$ tests remained non-significant. This could reflect either genuine structural similarity across domains or (more likely) insufficient power to detect real differences at $n = 8$.

3. Single random seed. All stochastic operations used seed $42$. Variance across seeds was not measured, limiting claims about result stability. Louvain community detection and power-law fitting are particularly sensitive to initialization, and a single seed captures only one realization of these stochastic processes.

4. Bipartite networks treated as unipartite. The drug-gene target network (ChG-Miner) is inherently bipartite (drugs and genes as distinct node types), but was analyzed as a unipartite graph for metric computation. This inflates some metrics (e.g., zero clustering coefficient is an artifact of bipartiteness, not a structural feature) and may distort classification.

5. Missing networks. The original configuration specified $10$ networks, but $2$ BioSNAP networks (ChSe-Miner and FF-Miner) did not produce valid results, reducing the sample to $8$. The side-effect and functional interaction domains are therefore absent from the analysis, narrowing its scope.

6. Size-confounding power. Several metrics show moderate Spearman correlations with network size ($|\rho| > 0.5$) but fail to reach significance at $n = 8$. With a larger sample, some of these metrics might be flagged as size-confounded, which would further reduce the number of interpretable structural features.

7. UMAP instability at small $n$. UMAP with $n = 8$ data points and $n_neighbors = 3$nneighbors=3 operates near the lower bound of meaningful embedding. The 2D layout is sensitive to parameter choices and should not be over-interpreted as reflecting true high-dimensional distances.

Conclusion

This exploratory characterization of $8$ pharmacological and social-baseline networks across $15$ topological metrics found no statistically significant differences between the $5$ interaction domains, even before multiple-testing correction. A Random Forest classifier achieved $62.5$ LOO-CV accuracy (versus $0$ stratified random baseline), with discriminative signal concentrated in domains that had multiple representative networks (social_baseline and protein_interaction). The most informative metrics were avg_clustering, powerlaw_xmin, and modularity.

The analysis provides an exploratory profile of structural variation across drug-drug interaction, drug-target, disease-disease, protein-protein interaction, and social network topologies. All computations are deterministic and fully reproducible via a pinned Docker environment (python:3.11-slim) with fixed random seeds. The pipeline, data acquisition scripts, and analysis code are designed to scale to larger network collections, where the statistical power limitations of this $n = 8$ study could be addressed.

The primary value of this work is methodological: it provides a reusable $15$-metric structural profiling pipeline for pharmacological networks, complete with multiple-testing corrections, size-confounding checks, and classification baselines. Future work with larger samples from each interaction domain would be needed to determine whether the observed topological patterns (e.g., high clustering in social networks, near-zero clustering in bipartite pharmacological networks) generalize beyond the specific networks analyzed here.