Amazon Product Co-purchase Network

Updated 8 July 2026

The Amazon Product Co-purchase Network is a set of product graphs derived from transactional signals and metadata, capturing joint purchase, review, and behavioral patterns.
Its multi-modal representations—from directed co-purchase to co-review graphs—support recommendation systems, representation learning, and causal network analysis.
Structural studies reveal dense local clustering, asymmetric motifs, and bias challenges, highlighting the need for debiasing and careful experimental design in network research.

The Amazon Product Co-purchase Network is a family of product graphs derived from Amazon transactional and metadata signals in which products are nodes and inter-product relations encode joint demand, shared buyers or reviewers, observed co-purchase, or inferred compatibility. In its explicit form, it is the directed network induced by Amazon’s “Customers Who Bought This Item Also Bought” feature; in later work it also appears as an undirected SNAP co-purchase graph, a co-review graph linking products that share reviewers, and a set of bipartite or sequence-based behavioral analogues that approximate co-purchase structure from user histories. Across these formulations, the network has served both as an empirical object for structural analysis and as an infrastructure for recommendation, representation learning, intention mining, and robustness analysis (Srivastava, 2010, Cao et al., 10 Aug 2025, He et al., 2024, Lu et al., 2022).

1. Graph definitions and data representations

At the most direct level, the network is a product–product graph whose vertices are products and whose edges reflect observed associations in Amazon’s recommendation interface or metadata. One study models the network as a directed graph extracted from Amazon’s “Customers Who Bought This Item Also Bought” feature, with a directed edge $i \to j$ when customers who bought product $i$ also often bought product $j$ (Srivastava, 2010). Another line of work uses the SNAP Amazon metadata collection and treats the graph as an unweighted, undirected product graph in which each edge indicates a co-purchase or similarity relationship (Cao et al., 10 Aug 2025). Related studies further derive product graphs from Amazon reviews, either by using co-buy records from Amazon Review Data or by linking products that share at least one reviewer (Xu et al., 2024, He et al., 2024).

Formulation	Edge semantics	Reported scale
Directed co-purchase graph	“Customers Who Bought This Item Also Bought”	262,111 nodes; 1,234,877 edges
Undirected SNAP co-purchase graph	co-purchase or similarity link	548,552 unique items; 1,788,725 undirected links
Multimodal co-buy subset	co-buy shopping record with accessible images	126,142 co-buy records; 107,215 products
Product co-review graph	products share at least one reviewer	about 65,000 nodes; 16.2 million edges

The underlying adjacency semantics vary substantially across studies. In the co-review setting, the adjacency matrix is defined by $[A]_{ij}=1$ if products $i$ and $j$ have at least one reviewer in common, with symmetry and no self-loops, while the weighted overlap $r_{ij}$ records the total number of shared reviewers (He et al., 2024). In sequence-based personalized search, Amazon purchase histories are converted into a bipartite successive behavior graph $G_{SB}$ in which product nodes connect to short-term sequence nodes whenever a product appears in a sequence, thereby serving as a behavioral analogue of a co-purchase network rather than a direct extraction of Amazon’s “also bought” graph (Lu et al., 2022). This multiplicity of representations is central: the term “Amazon Product Co-purchase Network” does not designate a single canonical adjacency rule, but a broader class of product networks derived from Amazon behavioral traces.

2. Structural organization and local graph patterns

Structural analyses of Amazon product networks emphasize strong local organization, large connected components, and non-random small subgraph patterns. In the March 02, 2003 Amazon/SNAP co-purchasing snapshot, the reported network statistics are 262,111 nodes, 1,234,877 edges, an average clustering coefficient of 0.4240, 717,719 triangles, a fraction of closed triangles of 0.2361, diameter 29, and 90-percentile effective diameter 11; the largest weakly connected component contains all nodes, while the largest strongly connected component has 241,761 nodes, or 0.922 of all nodes (Srivastava, 2010). These measurements indicate a graph that is locally dense and globally well connected.

Motif analysis reveals that local purchase patterns are highly asymmetric. Among 3-node directed motifs, Motif ID 4 is the most frequent at 217,566 occurrences, ahead of Motif 10 at 135,904, Motif 1 at 131,613, and Motif 3 at 104,071 (Srivastava, 2010). The interpretation given for Motif 4 is a converging structure in which two products point to a common product, suggesting that different purchase paths may collapse onto a smaller set of shared targets. For 4-node motifs, the most prominent patterns are again converging, particularly Motif IDs 59, 26, and 5. This suggests that local demand concentration is a recurring microstructural feature of the network.

More recent preprocessing studies on the SNAP metadata graph also report strong mesoscale organization. After removing products with missing information, one graph contains 519,497 nodes, 964,468 edges, and 159,575 isolated nodes; its largest connected component has 327,953 nodes and 902,604 edges. The same study reports 165,510 connected components in total, of which 5,935 are non-isolated, a power-law degree distribution, a power-law coefficient of 3.55 estimated via the CCDF in the largest connected component, a group assortativity coefficient of 0.327, and a Louvain modularity score of 0.926 (Liu et al., 3 Jun 2025). Taken together with the earlier motif results, this indicates that Amazon product networks are simultaneously sparse at the global level and highly clustered at local and community scales.

3. Similarity, complementarity, and substitutability

A central methodological issue is that co-purchase does not map cleanly onto a single semantic relation. Early item-based collaborative filtering treated the network implicitly through shared buyer overlap, using the Jaccard similarity

$J(p,c)=\frac{|U_p \cap U_c|}{|U_p \cup U_c|}$

between buyer sets of products $p$ and $i$ 0, and then ranking candidates by the maximum similarity to items already purchased by a user (Caruso et al., 2011). This formulation turns co-purchase behavior into a weighted item–item similarity graph, with edge weights approximated efficiently through linear counting, bitvectors, and one bitwise OR. It is effective for scalable item comparison, but it does not by itself distinguish substitutes from complements.

Subsequent work made that distinction explicit. A network perspective based on a bipartite product-purchase graph defines complements as products that occur in the same baskets significantly more often than expected, and substitutes as products that occur together significantly less often than expected but share similar complement sets (Tian et al., 2021). A supervised Amazon-scale model, Sceptre, operationalizes this separation by learning substitute and complementary edges from product text and observed Amazon link types. It treats “Users who viewed $i$ 1 also viewed $i$ 2” and “Users who viewed $i$ 3 eventually bought $i$ 4” as substitute supervision, and “Users who bought $i$ 5 also bought $i$ 6” together with “Users frequently bought $i$ 7 and $i$ 8 together” as complement supervision, over a corpus of 9.35M products, 144M reviews, 237M edges, and 21M users (McAuley et al., 2015). This indicates that Amazon’s observed product graph is heterogeneous even before any embedding is learned.

Metric-learning and embedding models sharpen the same point. A quadruplet network built from Amazon Clothing, Shoes, and Jewelry co-purchase data learns a shared latent space in which, for an anchor item $i$ 9, a similar item $j$ 0 should be closest, a complementary item $j$ 1 should be close but farther than $j$ 2, and a negative item $j$ 3 should be farthest, enforcing $j$ 4. The corresponding dataset contains 376,999 unique items and 3,693,416 quadruplets (Mane et al., 2019). Other work argues that complementariness is asymmetric and non-transitive, and therefore unsuitable for single-space symmetric embeddings; it introduces dual product embeddings and a directed complementary relation $j$ 5 learned directly from noisy purchase activities rather than from an explicit product graph (Xu et al., 2019). A related SGNS-based approach likewise uses the cross-space IN-OUT retrieval mode rather than same-space similarity, because within-space proximity tends to capture substitutability, whereas cross-space proximity better captures complementarity in co-purchase data (Kvernadze et al., 2022). A plausible implication is that the Amazon Product Co-purchase Network is best understood as a multiplex of relational semantics rather than a single notion of “relatedness.”

4. Representation learning and graph neural models

Modern work treats the network as a substrate for inductive representation learning, personalized retrieval, and cold-start recommendation. One personalized product-search model constructs a user successive behavior graph from short-term purchase sequences and applies jumping graph convolution to propagate information across high-order co-occurrence structure while resisting oversmoothing. It is evaluated on eight Amazon review subsets—Magazine, Software, Phones, Toys/Games, Instruments, Clothing, Health, and Home/Kitchen—and reports NDCG@10 gains over ZAM ranging from about 7.76% on Instruments to 41.39% on Health (Lu et al., 2022). Here the Amazon-like co-purchase signal is not a static product graph but a global behavioral network induced by shared sequence membership.

Attribute-aware network models further decompose co-purchase structure by product attributes. eRAN starts from an item co-purchase graph $j$ 6, derives attribute-specific subgraphs $j$ 7 by retaining only co-purchase edges whose endpoints share the same attribute value, embeds each attribute network with a deep autoencoder, and then applies attention to obtain a personalized item representation. On Amazon-Music, with 11,697 users, 7,100 items, 65,950 actions, and 2 features, eRAN reports Precision@5 of 0.1104, Precision@10 of 0.0691, Precision@15 of 0.0508, together with nDCG@5 of 0.4026, nDCG@10 of 0.4482, and nDCG@15 of 0.4671 (Liu et al., 2019). This shows that the co-purchase network can be factorized into attribute-specific explanations rather than treated as an undifferentiated graph.

Comparative GNN benchmarking on the SNAP co-purchase graph emphasizes the importance of inductive evaluation and rich node features. One study represents each product by a 601-dimensional feature vector formed from a 384-dimensional SBERT title embedding, a 10-dimensional one-hot group label, 7 standardized numeric metadata features, and a 200-dimensional dense category-path embedding, then evaluates LightGCN, GraphSAGE, GAT, and PinSAGE under a strict 80%/20% node split with no node overlap between train and test (Cao et al., 10 Aug 2025). The reported validation scores are: LightGCN AUC 0.8355 and AP 0.8592 with epoch time 569.17 s; GraphSAGE AUC 0.9976 and AP 0.9974 with epoch time 19.60 s; GAT AUC 0.9729 and AP 0.9888 with epoch time 2.29 s; and PinSAGE AUC 0.9562 and AP 0.9649 with epoch time 1881.00 s. A separate modified GraphSAGE system for new-item recommendation on the Amazon Product Co-Purchasing Network Metadata dataset retains only 1-hop structure, uses metadata such as title, group, and categories, and reports Top-5 accuracy of 0.0187 versus 0.0125 for a Random Forest baseline and 0.0063 for random sampling (Liu et al., 3 Jun 2025). These results suggest that the network has become not merely a similarity scaffold but a feature-rich inductive learning benchmark.

5. Semantic augmentation and purchase-intention distillation

A recent development is to treat the co-purchase network as the structural backbone for semantic inference rather than as an end in itself. MIND, “Multimodal Shopping Intention Distillation,” reformulates intention understanding as

$j$ 8

where $j$ 9 and $[A]_{ij}=1$ 0 are co-bought products, $[A]_{ij}=1$ 1 and $[A]_{ij}=1$ 2 are their images, $[A]_{ij}=1$ 3 and $[A]_{ij}=1$ 4 are their metadata or extracted features, $[A]_{ij}=1$ 5 is a commonsense relation from ConceptNet, and $[A]_{ij}=1$ 6 is an LVLM, specifically LLaVa-1.5-13B in the reported experiments (Xu et al., 2024). The Amazon Product Co-purchase Network here supplies the product-pair edges, and the model generates natural-language purchase intentions for those edges.

Using Amazon Review Data from Ni et al. (2019), focused on Electronics and Clothing, Shoes and Jewelry, the method constructs a multimodal intention corpus containing 126,142 co-buy shopping records, 107,215 products, and 1,264,441 intentions across 20 ConceptNet relations after filtering out products without accessible images (Xu et al., 2024). The pipeline first extracts multimodal product features such as attribute, design, quality, and likely use from images and product names or metadata. It then prompts the LVLM with both product images, both products’ extracted details, and a ConceptNet relation, instructing the model to act as the customer and infer why the products were purchased together. A human-centric role-aware filter subsequently retains only intentions judged likely to motivate joint purchase.

The resulting artifact is a multimodal intention knowledge base in which each co-buy edge is expanded into one or more intention statements همراه with relation labels and multimodal evidence. The appendix reports that only 46.7% of generations passed the final filter; among discarded cases, 81.0% were plausible but not strong enough to motivate purchase, 13.0% were rejected due to LVLM misjudgment, and 6.0% were implausible or factual errors (Xu et al., 2024). On 5,000 sampled intentions, intrinsic human evaluation reports plausibility of 94%, typicality of 90%, human-centric correctness of filter of 82%, filter rationale correctness of 80%, pairwise agreement of 73.1%, and Fleiss’s $[A]_{ij}=1$ 7. Downstream, fine-tuning on MIND-generated data improves IntentionUnderstanding and IntentionUtilization on IntentionQA, for example raising LLaMA2-7B-chat to 66.15 average on understanding and 59.04 average on utilization, and Mistral-7B-Instruct-v0.2 to 76.97 and 62.02 respectively. This makes the co-purchase network a semantic knowledge substrate: the graph no longer states only what was bought together, but also models why it may have been bought together.

6. Bias, manipulation, and causal reinterpretation

A persistent methodological concern is that observed Amazon product links are behavioral traces, not uncontaminated indicators of preference or compatibility. In fake-review detection, products that buy fake reviews are shown to cluster in distinctive regions of a product co-review network whose nodes are products and whose edges indicate at least one shared reviewer. On a network of about 65,000 nodes and 16.2 million edges, degree, eigenvector centrality, PageRank, and clustering coefficient become predictive features in a random-forest classifier, and unsupervised K-means clustering with $[A]_{ij}=1$ 8 identifies communities with high concentrations of fake-review buyers, typically marked by high degree, PageRank, eigenvector centrality, and sometimes high clustering coefficient (He et al., 2024). The reported correlations also show that degree and PageRank are almost perfectly correlated at approximately 0.99, and degree and eigenvector centrality at approximately 0.92, while clustering coefficient is less tied to textual and rating-based variables. This indicates that network topology captures manipulation-relevant structure that is not reducible to review content or metadata.

Recent causal work extends the same skepticism to co-purchase edges themselves. Cadence introduces an Unbiased Asymmetric Co-purchase Relationship, or UACR, to build a deconfounded directed item graph that removes item popularity bias and user-attribute confounding before using LightGCN-based propagation and counterfactual exposure to improve diversity (Zhang et al., 19 Dec 2025). The framework trains with Bayesian Personalized Ranking,

$[A]_{ij}=1$ 9

and derives a theoretical norm–popularity relation $i$ 0, supporting the claim that raw item embeddings tend to track popularity. The reported Wilcoxon signed-rank statistic of 15.0 with $i$ 1 indicates significant improvements over the best baselines at the 5% level. This suggests a broader reinterpretation of the Amazon Product Co-purchase Network: it is not only a descriptive or predictive graph, but also a biased observational object requiring debiasing, causal adjustment, and careful experimental design.

Methodological caution appears as well in benchmarking practice. Inductive node-disjoint evaluation has been adopted precisely because transductive or edge-based splits can leak node identity or neighborhood structure and yield unrealistically high pre-training scores (Cao et al., 10 Aug 2025). A recurring misconception is therefore that any co-purchase graph can be treated as a neutral similarity network. The literature instead shows three persistent complications: complementarity and substitutability are distinct; many useful relations are directional rather than symmetric; and observed links are shaped by popularity, exposure, and manipulation. The Amazon Product Co-purchase Network is accordingly best viewed as a rich but noisy behavioral graph whose meaning depends on the edge construction, the downstream task, and the inferential assumptions imposed upon it.