Turning Sparse Relationship Data into a Complete Economic Map

How RedGraphs Estimates Hidden Money Flows Between Companies

“If only five percent of company relationships have actual reported dollar values, what’s the value of estimating the other ninety-five?”

Every relationship in our dataset is real. Each one comes from verified public disclosures confirmed by S&P Global, representing genuine customer and supplier links where money changes hands. The only missing piece for most relationships is how much money changes hands.

Ignoring those 95% of links would be like trying to model the economy by looking only at companies that disclose their top customers. You would be missing almost all of the structure. Our job is to fill in the blanks, not by guessing, but by applying a rigorous mathematical method called Iterative Proportional Fitting (IPF). This patented approach lets us estimate the most likely money flows across the entire network in a way that is consistent, auditable, and grounded in financial reality.

We also ensure there is no forward-looking bias. Every estimate is calculated strictly based on the information available at that moment in time, just as it would have been seen by the market on that date. It is a true point-in-time network.

What We Are Estimating

Imagine the economy as a giant network of companies, each one a node, and every transaction between them a link. Formally, let G = (V, E) be a directed graph where each edge (i, j) in E represents a flow of money from supplier i to customer j. We want to estimate the dollar value for every link.

We know some of these values directly, denoted , but most are missing. We also know each company’s total revenue and cost of goods sold, which give us row and column sums that all flows must satisfy. The goal is to fill in the unknowns in a way that is mathematically consistent with those totals.

• Respects known values for reported relationships
• Matches each company’s total revenue and spend
• Remains as close as possible to a prior belief about the intensity of each link (based on text, filings, or similarity)

How IPF Works

RedGraphs estimates a nonnegative flow matrix that satisfies accounting constraints and fixes any disclosed transactions:

To recover missing values, we solve a weighted divergence minimization with temporal smoothing against a prior :

Here are confidence weights from document provenance, disclosure frequency, and semantic certainty. The term with enforces temporal coherence with the prior period network .

The solution retains the multiplicative IPF structure with scaling multipliers that enforce exact totals:

where and are updated by alternating row and column scaling until convergence. The result is a unique, balanced, and time-consistent matrix of inter-company money flows suitable for backtesting and audit.

The Algorithm in Simple Terms

1. Start with what you know. Initialize everywhere and lock in any actual reported values.
2. Scale each supplier. Adjust rows so each company’s outgoing flows add up to its total revenue.
3. Scale each buyer. Adjust columns so each company’s incoming flows add up to its total cost or spend.
4. Repeat until balance. After a few iterations, everything converges to the maximum-likelihood configuration of flows.

Why This Matters for Investors

1. Complete coverage: Estimating missing values reveals the true network topology and hidden dependencies that filings alone cannot show.
2. Accounting consistency: IPF enforces hard balance constraints so portfolio-level exposures aggregate perfectly to reported financials.
3. Signal discovery: A dollar-weighted network lets analysts trace shocks, measure concentration risk, and compute contagion and centrality metrics.
4. No forward bias: The network is built with point-in-time logic, ensuring historical accuracy for backtesting.
5. Auditability: Every estimated flow can be traced to its constraints, priors, and convergence steps.

No Forward Bias: Point-in-Time Precision

All estimates are built using a strict two-axis point-in-time framework. One axis tracks when a document was published and first processed, and the other records the periods covered in that document. This means you can build a network as of May 2025 using only documents known by that date, even if they reference earlier years.

What This Unlocks

• Event propagation: Model how revenue surprises spread through supply chains.
• Concentration risk: Identify fragile networks or overexposed suppliers.
• Network momentum: Weight classic factors by upstream and downstream dollar centrality.
• Scenario testing: Simulate shocks, policy changes, or demand shifts in seconds.

Closing Thoughts

Estimating unknown values is not about guessing—it is about completing the picture. IPF gives us a mathematically sound, economically faithful way to infer hidden money flows between companies, producing a network that is both realistic and analytically powerful.

Once the network is complete, it becomes a living map of the global economy that lets you trace shocks, measure dependencies, and find alpha in the most unlikely places.

That is the beauty of RedGraphs: turning sparse public data into a coherent, measurable, and investable model of how money actually moves through the world.