Quantifying Circularity in AI Industry Deal Networks

The rapid growth of the AI industry has led to huge amounts of capital flowing among multitudes of different technology companies, venture capital firms, and cloud infrastructure providers. Between the years 2022 and 2025, AI companies have received investments upwards of $100 billion dollars, furthermore, cloud service commitments have reached into the hundreds of billions of dollars (CB Insights, 2024; Bloomberg, 2025).

An important consequence of this capital growth is the emergence of reciprocal relationships between investors and investees. For example, there are cloud providers that invest equity in AI startups, who subsequently commit to purchasing cloud services from the same investors. Hardware manufacturers also invest in cloud infrastructure companies, who then purchase the manufacturer's products. These bidirectional flows create what we call circular patterns. These are closed loops where value circulates between parties through different transaction types.

While these circular deals may simply be a result of rational business strategy and vertical integration, they bring up important questions for financial analysts, regulators, and investors. Namely, how should “organic” revenue growth be evaluated when a substantial amount of a company's revenue comes from entities in which it holds equity positions? What are the risk correlations among companies whose valuations depend on contracts with one another?

This paper offers five contributions. First, it will present a formal methodology for representing corporate deal structures as directed graphs to detect and visualize circular flows. Second, it introduces the Loop Score, a composite metric that measures the strength of direct, two-party relationships based on flow type diversity, monetary balance, and data quality. Third, the paper extends this framework to detect and measure multi-party cycles, circular flows involving three or more companies, using depth first search with a complementary Cycle Score metric. Fourth, the paper introduces the Hub Score, which aggregates participation across both two-party loops and multi-party cycles to identify companies that are central to the industry. Fifth, the paper applies this methodology to a curated dataset of 90 deals among prominent AI, cloud, and semiconductor companies, to identify circular structures as well as the hub companies that occupy central positions within this network.

The current AI industry is characterized by a high degree of role overlap among its largest participants. Cloud infrastructure providers also act as investors, compute suppliers, and customers of the companies they invest in. This structural feature, combined with rapid capital growth and increasing market concentration (Stanford HAI, 2024; Vipra & Korinek, 2023), creates conditions where circular capital flows may emerge at scale. Understanding these patterns and their broader implications requires drawing on three bodies of literature: network analysis in financial systems, related-party transaction analysis, and venture capital and platform economics.

Graph-based methods have been widely used within financial models. Allen & Gale (2000) created the foundational model of financial contagion, showcasing how shocks can propagate through interbank lending networks via direct balance sheet linkages. This is a mechanism that the paper then adapts to analyze how valuation shocks might cascade and propagate through investor-investee relationships in AI deal networks. Gai & Kapadia (2010) extended this framework to showcase how highly interconnected nodes can create systemic fragility. The Hub Score method, which quantifies the extent of a company's participation in circular flows, is based on their concept of interconnected institutions. Acemoglu et al. (2012) demonstrated that shocks to central firms can propagate into aggregate fluctuations when network connections are asymmetric, a dynamic this paper examines in the context of AI deal networks.

Previous financial literature has studied related-party transactions and how they can affect financial statement quality. Gordon et al. (2004) documented that related party transactions are associated with weaker governance and lower earnings quality; this is a framework directly applicable to the Microsoft-OpenAI relationship, where Microsoft holds equity and receives cloud revenue from OpenAI, where it holds a significant equity position. Dechow et al. (2011) identified financial statement patterns predictive of material misstatements, including unusual revenue growth from related parties. While this paper does not assess the legitimacy of any specific transaction, the Loop Score draws on a similar analytical intuition: that bidirectional flows between related parties warrant closer examination. Circular trading patterns have been studied in equity markets for manipulation detection (Aitken et al., 2015). The paper extends this literature by providing a quantitative framework for detecting circular patterns across heterogeneous transaction types (equity, services, hardware) rather than within a single asset class.

Venture capital literature has documented extensive syndication networks. Hochberg, Ljungqvist & Lu (2007) demonstrated that VC network centrality predicts fund performance, establishing that investor relationships have real economic consequences beyond capital provision. The AI industry exhibits an intensified version of this phenomenon: cloud providers are not merely investors but also customers and infrastructure suppliers to the companies within their portfolio. This creates multilayer dependencies that are far more concentrated than those usually seen in traditional VC syndication.

Platform economics offers additional theoretical grounding. Rochet & Tirole (2003, 2006) formalized two-sided market dynamics where platforms subsidize one side to capture value from another. Cloud providers investing in AI startups who then consume cloud services exemplifies this logic: equity investments may also have the added function of customer acquisition costs, with returns captured through service revenue rather than traditional exit multiples.

To collect the needed data, a curated dataset of 90 deals spanning across 28 companies was constructed from publicly available sources including SEC filings, official press releases and financial news reporting from sources such as Bloomberg, Reuters, CNBC, and The Information. The data collected spanned from January 2022 to January 2025.

The sample companies were selected based on three criteria:

This dataset was purposefully selected and prominent participants within the industry were used. It is not a random sample of the AI ecosystem. These findings should be interpreted as patterns among the specific dataset and not a comprehensive population estimate.

Each deal record includes the following attributes:

The paper models the deal network as a directed multigraph G = (V, E), where V represents companies and E represents directed edges from deals. Each edge e ∈ E is characterized by:

When multiple deals share the same source and target companies, they are aggregated into a single edge. Deals involving multiple parties of the same role (e.g., three co-investors in one round) are represented as separate edges. Direction is inferred from party roles: INVESTOR - INVESTEE, CUSTOMER - SUPPLIER, ACQUIRER - TARGET. Partnership deals without clear directionality are represented as a single edge with a non-directional flag; these edges do not generate reverse edges and therefore cannot independently produce loops.

The paper defines a two-party loop as a pair of edges (e₁, e₂) where e₁ connects company A to company B, and e₂ connects B to A. This can be expressed formally with:

Two-party loop detection is performed by constructing an edge index keyed by (from, to) pairs and checking for the existence of reverse edges. This algorithm runs in O(|E|) time. Two-party loops represent the simplest form of circularity—direct reciprocal flows between two entities.

In order to actually quantify the strength and significance of the detected two-party loops, the paper introduces the Loop Score, a composite metric in the range [0, 1] that combines three factors:

The weighting scheme (α = β = 0.35, γ = 0.30) was selected to balance structural characteristics (diversity, balance) against data quality considerations. We provide empirical sensitivity analysis in Section 6.3, demonstrating ranking robustness across alternative weighting schemes with further justifications.

To quantify company-level centrality in circular flows, the paper defines the Hub Score as the sum of scores across all circular structures which includes both two-party loops and multi-party cycles - in which a company participates:

The Hub Score captures systemic importance: companies with high Hub Scores are entangled in multiple reciprocal relationships. As established before this suggests that disruptions to these companies could propagate through several circular flows simultaneously causing effects across the entire dataset (market).

While two-party loops capture direct reciprocal relationships, value may also circulate through longer chains that extend beyond direct exchanges. We extend the analysis to detect multi-party cycles: circular flows involving three to five companies. The upper bound of five reflects both analytical and computational considerations: cycles of length six or greater are unlikely to represent cohesive circular relationships given the network's size, and the number of candidate paths grows combinatorially with cycle length.

Formally, a k-party cycle is an ordered sequence of k distinct companies (C₁, C₂, ..., Cₖ) such that directed edges exist connecting each consecutive pair and closing the loop:

Detection is performed using depth-first search (DFS) from each node, following Tarjan's (1972) foundational algorithm for graph traversal. The paper explores paths up to length k and checks for edges that return to the starting node. To avoid counting the same cycle multiple times from different starting points, the paper canonicalizes cycle identifiers by selecting the lexicographically smallest rotation of company slugs, a standard technique in cycle enumeration (Johnson, 1975).

The weights chosen for the Cycle Score differ from the Loop Score to account for the structural properties of multi-party cycles. The length penalty (L) prioritizes shorter cycles, as a 3-company circular arrangement represents a tighter, more direct form of interdependence than longer chains. Value magnitude (M) receives reduced weight (0.10 vs 0.35 in loops) since multi-party cycles naturally increase the amount of value as it passes through edges. As with the Loop Score, these weights were selected heuristically; Section 6.3 demonstrates ranking robustness across alternative weighting specifications.

A critical question in network analysis is whether observed patterns are actually statistically meaningful or merely caused due to network density. To address this, The paper uses the configuration model - a well-established null model in network science that generates random networks preserving the degree sequence of the original graph (Newman, 2010; Molloy & Reed, 1995).

Algorithm. The implementation uses the stub-matching variant with Fisher-Yates shuffling:

What the null model preserves vs. randomizes:

Statistical inference. The method runs 500 iterations of the configuration model, counting the loops and cycles in each randomized network. This generates a null distribution against which it compares the observed values. Statistical significance is assessed using z-scores (standard deviations from null mean) and two-tailed p-values derived from the normal approximation:

A p-value below 0.05 indicates the observed count is unlikely to arise by chance in a random network with the same degree sequence. This result would suggest that the pattern reflects genuine structural properties of the AI industry rather than network density artifacts.

The constructed graph contains 28 nodes and 77 directed edges. The detection algorithms have identified 35 circular structures in total:

The prevalence of multi-party cycles (28) substantially exceeds two-party loops (7), indicating that circular value flows in the AI industry frequently traverse intermediary nodes rather than flowing directly between counterparties.

Table 2 presents the detected loops ranked by Loop Score. The detected loop score's cluster within a narrow band (0.78–0.85). This indicates that the detected loops are comparable in strength rather than dominated by a single outlier pair. The results show that Cloud providers and infrastructure companies appear in nearly every loop. This is consistent as they hold dual roles as both investors and service recipients. The highest-scoring loops show flow type diversity, different transaction types in each direction, and high source confidence. Crucially, a large portion of detected loops default to the minimum Balance Ratio of 0.50 due to undisclosed monetary amounts on at least one edge. This shows that the loop score of these pairs are driven primarily by flow diversity and confidence rather than verifiable monetary symmetry.

Transaction amounts in Table 2 reflect disclosed or projected totals and span varying time horizons. Multi-year cloud commitments and projected investment maximums are not annualized; readers should exercise caution when comparing amounts across deal types.

A crucial question for this analysis is whether the observed circular loops are statistically meaningful or are simply caused due to network density. If a random network of companies with similar deal volumes produce similar loop counts, the findings would be unremarkable. To address this, the paper applies the configuration model (Section 3.7), generating 500 random networks that preserve each company's deal count while randomizing the partners that each company constructs deals with.

Null hypothesis: The observed loop and cycle counts are consistent with what would emerge by chance in a random network with the same degree distribution. Alternative hypothesis: These companies exhibit more circular patterns than random expectation, suggesting intentional reciprocal structuring of deals.

Interpretation of results:

Two-party loops (direct reciprocity): The observed 7 bidirectional loops is 152.3% higher than random expectation (null mean = 2.8 ± 1.2). With z = 3.41 and p < 0.001, the observed loop count is largely different from random expectation. A result this extreme would occur in fewer than 0.1% of random networks under the null hypothesis. This indicates that these companies form direct reciprocal relationships (investor - customer, supplier - client) at rates that exceed what would occur in randomly rewired networks with the same degree sequences.

Multi-party cycles: The 28 observed cycles is consistent with random baseline levels (exact p = 0.21). The high variance in the cycle null distribution (SD = 9.9) reflects the combinatorial sensitivity of longer cycles to random edge placement, making statistical significance harder to establish for multi-party structures. Longer circular chains are common in dense networks and could plausibly arise in randomly rewired networks.

Case 1: Microsoft–OpenAI (Score: 0.83). Microsoft has invested an estimated $10 billion into OpenAI equity. OpenAI has also commited $250 billion to Microsoft Azure cloud services which was part of restructuring a cumulative multi-year obligation and not a single-period payment. This case study represents an example of investor-customer circularity. Equity flows from cloud provider to AI company, and cloud revenue flows back to the orginal cloud provider. The high score reflects cross-type flow diversity (money vs. services) and strong source confidence, despite the substantial asymmetry between investment and cloud commitment amounts.

Case 2: NVIDIA–xAI (Score: 0.78). NVIDIA invested $2 billion in xAI. xAI then committed and purchased an estimated $20 billion in NVIDIA GPUs for its Colossus 2 supercomputer. This is another clean investor-customer loop: equity flows from hardware manufacturer to AI company, and hardware purchase revenue flows back. The relationship is a perfect example of Acemoglu et al.'s (2012) supply chain propagation mechanism: a shock to NVIDIA would impair xAI's infrastructure buildout, while reduced xAI demand would affect NVIDIA's revenue. This would create a feedback loop that propagates.

Case 3: Google–Anthropic (Score: 0.80). Google invested $5.3 billion in Anthropic across multiple rounds of investment. Anthropic then committed to an estimated tens of billions of dollars in Google Cloud spending. Note that the precise figure has not been publicly confirmed. Similar patterns exist with Amazon's $8 billion Anthropic investment and further AWS cloud commitments. This competing investment structure: where rival cloud providers invest in the same AI companies creates parallel circular flows through a common node. The Loop Score reflects cross-type flow diversity and high source confidence, though the Balance Ratio defaults to 0.50 due to the undisclosed cloud commitment amount, consistent with the pattern noted in Section 4.2.

Table three displays companies ranked by their Hub Scores. It aims to quantify their systemic centrality in the circular flow network. Companies with higher Hub Scores participate in more or have stronger circular relationships.

Microsoft achieves the highest Hub Score (28.82), reflecting participation in 35 circular flows. This positions Microsoft as the most systemically central entity in the AI deal network.

We also see from the table that NVIDIA occupies a unique structural position: it simultaneously serves as hardware supplier (GPUs to cloud providers), equity investor (stakes in xAI, OpenAI, and others), and customer (renting cloud capacity). This multi-role centrality suggests that NVIDIA's financial performance is very much interconnected with the broader AI ecosystem. Microsoft and Anthropic also rank highly, showing that they all occupy central roles as cloud provider-investor and multi-cloud investee respectively.

Beyond two-party loops, the paper also considers 28 multi-party cycles involving three or more companies. Table 4 displays the highest-scoring cycles, which reveal more complex patterns of circular value flow.

Several patterns can be seen from the multi-party cycle analysis. First, NVIDIA appears in the majority of high-scoring cycles. This shows its role as a critical intermediary: companies pay NVIDIA for hardware, NVIDIA invests in cloud providers, and those providers sell services back to the original hardware purchasers. Second, cycles involving AI model companies (OpenAI, Anthropic) often include both their cloud providers (Microsoft, Google, Amazon) and the hardware suppliers (NVIDIA), creating triangular dependencies between the providers and companies.

The existence of 28 multi-party cycles, substantially exceeding the 7 two-party loops, suggests that circular value flows in the AI industry are frequently mediated by intermediary nodes. This has some implications for systemic risk: disruptions to hub nodes like NVIDIA could simultaneously affect multiple circular flows of varying lengths.

The circular patterns the paper documents are not inherently problematic. Vertical integration, strategic partnerships, and reciprocal business relationships are all very common features of current technology industries. Cloud providers who invest in AI companies who then become cloud customers could simply be rational customer acquisition strategy. This is consistent with Rochet & Tirole's (2003) two-sided market framework, where companies aim to subsidize one side to capture value from the other. Furthermore, hardware companies that invest in infrastructure providers naturally creates more demand for their hardware products.

However, the scale and prevalence of these patterns in the AI industry and the size of the Loop Scores the paper computes suggests that analysts should consider circularity when evaluating company financials and markets. The patterns the paper outlines concerns raised by Gordon et al. (2004) regarding related party transactions. When revenue is dependant from entities in which a company also shares equity relationships, traditional financial statement analysis requires adjustments.

A crucial finding from the null model analysis (Section 4.3) is the large difference between two-party loop significance and multi-party cycle significance. Two-party loops are highly significant as the observed 7 loops greatly exceed the null expectation of 2.77 under the configuration model. However, the 28 observed multi-party cycles do not have much statistical significance (z = 1.25, p = 0.21), despite exceeding the null mean of 15.66 by 79%.

This divergence between two party loops and multi party cycles has several interpretations. First, it may reflect a genuine structural property of the AI deal network: companies deliberately form tight, bilateral reciprocal relationships (investor becomes customer, and vice versa), but the longer chains that creates multi-party cycles are formed as coincidental byproducts of network density rather than intentional circular structuring by firms. Under this interpretation, the two-party loop is the primary unit of circular behavior, and multi-party cycles are secondary.

It can also be understood that the divergence may be a statistical artifact of the cycle null distribution's high variance (SD = 9.89 relative to a mean of 15.66, yielding a coefficient of variation of 0.63). Longer cycles are combinatorially sensitive to random edge placement: small changes in which companies are connected can produce large swings in cycle counts. This dispersion makes it inherently difficult to establish statistical significance for multi-party structures, even when observed counts meaningfully exceed the null mean. To mitigate this, a larger dataset or a more constrained null model may resolve whether the cycle count is genuinely elevated.

Finally, the two metrics may capture different aspects of circularity. Two-party loops detect direct reciprocity;the simplest and most unambiguous form of circular flow. Multi-party cycles however, detect systemic connection, which is valuable for risk assessment but may not require statistical significance to be analytically meaningful. The 28 detected cycles still represent concrete pathways through which value circulates among AI companies; whether they exceed random expectation is a separate question from whether they matter for systemic risk.

The findings have several implications:

The paper's findings parallel and diverge from prior financial network analyses. Unlike Gai & Kapadia's (2010) interbank networks, where linkages are homogeneous (lending relationships), AI deal networks exhibit heterogeneous edge types—equity, services, and hardware flow through the same nodes simultaneously. This multi-layer structure means that a company can be a creditor (investor), debtor (cloud customer), and supplier all within a singular relationship. This complicates the contagion dynamics that Allen & Gale (2000) modeled for single-layer networks.

The Hub Score can be used to extent Acemoglu et al.'s (2012) centrality measure by incorporating participation across circular structures rather than counting direct connections. While Acemoglu et al. shows that shocks to central nodes propagate downstream, the AI network's circular topology means that shocks can return to their origin. NVIDIA's difficulties could impair xAI (as both investor and GPU supplier), whose decreased infrastructure spending impacts NVIDIA's revenue, while simultaneously affecting OpenAI's Azure consumption which impacts Microsoft, which may then reduce investment in NVIDIA-dependent startups.

Dechow et al. (2011) used financial ratios to identify accounting misstatements. The Loop Score applies a similar logic to deal structures: rather than examining financial statements, it flags company pairs that exchange value in both directions. A high Loop Score does not indicate fraud, but it identifies the relationships most likely to raise the related-party concerns documented by Gordon et al. (2004).

Traditional venture capital networks, as studied by Hochberg et al. (2007), involve investors who co-invest but rarely transact with their portfolio companies beyond providing capital. The AI deal network differs in that cloud providers serve as investors, customers, and infrastructure suppliers to the same companies simultaneously. This overlap of roles creates tighter interdependencies, which may explain why AI company valuations appear more correlated than those in traditional VC portfolios.

The Loop Score is this paper's primary contribution. It is the only metric whose results are statistically significant (z = 3.41, p < 0.001), and it provides a simple, repeatable way to flag investor-customer pairs with reciprocal flows that may warrant closer scrutiny.

The Cycle Score and Hub Score serve supporting roles. The Cycle Score detects longer circular chains (3–5 companies); the 28 detected cycles, while not statistically significant, identify real pathways through which value flows beyond direct counterparties. The Hub Score sums a company's participation across all circular structures to measure how central it is to the network. Together: the Loop Score shows where reciprocity is strongest, the Cycle Score shows how value moves through intermediaries, and the Hub Score shows which companies are most involved. All three metrics' weights can be adjusted for different uses.

The Loop Score weights (α=0.35, β=0.35, γ=0.30) and Cycle Score weights were determined heuristically. To assess robustness, all scoring calculations were re-ran under five alternative weighting schemes and compared the resulting rankings.

This paper establishes:

This paper does not establish:

Future work could extend this analysis by: (1) incorporating temporal dynamics to study how circular structures form, strengthen, and dissolve over time; (2) developing causal inference methods to assess whether circularity affects financial outcomes; (3) applying the methodology to historical technology sectors for baseline comparison; (4) exploring weighted cycle detection that accounts for edge importance rather than treating all edges equally; (5) developing real-time monitoring systems that flag emerging circular patterns as deals are announced.

This paper has presented a methodology for quantifying circularity in corporate deal networks and applied it to the AI industry (2022-2026). Three metrics were introduced: the Loop Score for two-party bidirectional flows, the Cycle Score for multi-party circular chains, and the Hub Score for identifying systemically central entities. Analyzing 90 publicly reported deals among 28 companies, the paper identified 35 circular structures: 7 two-party loops and 28 multi-party cycles.

The central finding is that two-party loops: direct reciprocal relationships between investor-customer pairs—occur at rates that significantly exceed random expectation (z = 3.41, p < 0.001). These bilateral circular patterns are a statistically significant structural feature of the AI deal network, not merely an artifact of network density. The 28 detected multi-party cycles, while not statistically significant against the null model, identify additional pathways through which value circulates among companies via intermediary nodes.

Infrastructure providers - particularly Microsoft and NVIDIA - occupy central positions in these circular flows, serving simultaneously as investors, cloud providers, and customers within the same network. The Hub Score quantifies this centrality, highlighting the companies whose disruption could affect multiple circular flows simultaneously.

The paper does not claim these patterns constitute market manipulation or indicate a “bubble” in any technical sense. Such determinations would require causal analysis beyond the scope of this study. Rather, the paper provides tools for analysts, regulators, and researchers to identify and quantify circular relationships that may warrant closer examination.