METRIC i.
Loop Score
L(a,b) = Σ wᵢ·wⱼ ∀ i:a→b, j:b→a
Pairwise circularity between two companies. Captures the canonical “A invests in B, B buys from A” relationship, summed over deal weight in both directions.
Working PaperVol. 01 · No. 01
A working paper on financial circularity in artificial-intelligence markets.
May 202632 pp.
WP / 2026.05 · Network FinanceJEL · G32 · L86 · D85
A study of financial circularity, 2022–2025Capital that returns to its source.
Measuring capital that flows in loops across the AI industry.
Figure 01Sample network — featured cycle C-01
Capital / equity
Compute hardware
Cloud service
n = 28 · m = 90
28
Companies in sample
AI · cloud · semiconductor
90
Deals analyzed
2022 – 2025
35
Circular structures
7 loops · 28 cycles
3
Quantitative metrics
Loop · Cycle · Hub
The artificial-intelligence industry has experienced unprecedented levels of capital growth, with major technology companies participating in complex webs of investments, cloud-service commitments, and hardware supply agreements. This paper presents a novel methodology to measure and quantify the flow of circular deals in corporate ecosystems — instances where capital or value flows between companies through different mechanisms, creating loops of different lengths.
Three complementary metrics are introduced: the Loop Score, which measures circularity between company pairs; the Cycle Score, which tracks multi-party cycles involving three or more companies; and the Hub Score, which aggregates participation across all circular structures to identify systemically central entities.
Across 90 deals among a curated set of 28 prominent AI, cloud, and semiconductor companies from 2022–2025, we identify 35 total circular structures consisting of 7 two-party loops and 28 multi-party cycles. Findings show that circular patterns are common among major AI companies in the sample, with certain infrastructure providers participating in numerous circular flows.
Implications are discussed for revenue recognition, valuation interdependence, systemic-risk assessment, and market transparency.
§ 02 / METHODOLOGY
Three complementary metrics
How we measure money that flows in circles.
Every circular structure has a length and a set of participants. The metrics decompose the network into pairwise loops, multi-party cycles, and a per-firm centrality measure derived from both.
METRIC ii.
Cycle Score
C(k) = Σ ∏ wₑ over directed cycles of length k ≥ 3
Multi-party cycles. Tracks loops where capital moves through three or more firms before returning. Length-weighted product of edge magnitudes preserves the strength of long indirect paths.
METRIC iii.
Hub Score
H(v) = Σ 1{v ∈ s} · score(s) ∀ structures s
Per-firm centrality. Aggregates a company's participation across every loop and cycle it belongs to. Identifies infrastructure providers that sit at the center of many independent circular flows.
Formal definitions, edge-weighting scheme, and treatment of bidirectional deals appear in § 2 of the methodology.
§ 04 / FINDINGS
Summary of results.
Selected results from the 28-company, 90-deal sample. Full tables and sensitivity analyses appear in the paper.
i.
Two-party loops are concentrated among hyperscalers and model labs.
All seven identified two-party loops involve at least one cloud provider on one side and an AI model lab or chip manufacturer on the other.
7two-party loops
ii.
Multi-party cycles dominate the network.
80% of identified circular structures are 3+ company cycles, suggesting risk is harder to detect by examining bilateral relationships alone.
28multi-party cycles
iii.
Hub Score is heavily skewed.
The top three firms by Hub Score participate in over half of all circular structures in the sample, indicating systemically central infrastructure providers.
3firms · 50%+ share
iv.
Cycle length grows with valuation.
Average cycle length increases monotonically with combined participant valuation — longer cycles surround the most-valued firms.
4.2avg. cycle length
FEATURED CASE / C-01
The OpenAI · Microsoft · NVIDIA triangle.
A worked example of a length-3 cycle. Microsoft's equity in OpenAI returns as Azure commitments; OpenAI's GPU spend returns to Microsoft via NVIDIA's data-center sales.
Read case study →FIG. 02 / CYCLE C-01
FIG. 02 Schematic of cycle C-01. Edge color indicates flow type: green for capital, pink for compute hardware, blue for cloud service. Edge weights omitted; see Table 4 in the paper.