Why most links are noise

A graph of public records is simple to describe. Each company, person, address and public body is a node. Each directorship, shareholding, registered address, contract or filing is an edge. Load a few registers and you have millions of edges: the UK's company register alone added 193,789 companies in the three months to September 2026. Soon there is a path between almost any two names you care to type.

That is the problem. A graph in which everything is connected says nothing. Most edges are true but uninformative. Five difficulties decide whether such a graph shows something real or only that everyone knows everyone: hubs, time, identity, provenance and the choice of path. This note sets out principles, not a particular system. All entities in the examples are invented.

1. Hubs

Some nodes touch a large share of the graph for reasons unrelated to control. A formation agent lends its office address to thousands of companies. In some offshore jurisdictions every company must keep a registered office there, and providing one is a licensed business, so the same few providers appear in the records of a great many companies. Large auditors, banks, law firms and public bodies appear in the records of countless unrelated companies.

These edges are real, but a path through a formation agent's address says only that two companies used the same paperwork service. In graph terms these are nodes of very high degree, and treated like any other node they put almost every pair of companies two or three steps apart.

Removing hubs outright is tempting and wrong: sometimes the agent is the story, and a small address shared by a handful of firms differs from one shared by thousands. What works is weighting by degree: the more nodes an intermediary touches, the less a path through it should count. Public bodies need their own treatment: "both companies filed with the same tax office" is almost never informative; "both won contracts from the same small agency in the same month" may be.

2. Time

Every edge has dates, stated or implied. A directorship runs from appointment to resignation; a shareholding from purchase to sale; an address until the company moves. A graph that drops the dates treats every relation as permanent and finds connections that never existed on any single day.

Our rule is strict: a path counts as a connection only if it is time-respecting, meaning every step held on the same day. If Person X left Company A before Person Y joined, X and Y were never colleagues there, however short the path looks.

The broken path is not worthless. "Y took over a company X had run" can matter, especially when it repeats across companies. But it is a succession, not a connection, and should be described as one. Two more points follow. Missing end dates are common, and an open-ended edge should not be read as "still true today" without checking. And timing is often the finding itself: a company formed weeks before a contract, or a stake moved just before a reporting date, is visible only if every edge carries its dates.

3. Identity

A graph is only as good as its nodes. Deciding whether two records describe the same person or company, entity resolution, is a subject of its own, covered in our notes Decisions, not text and Why search stays at the surface. For a graph, two consequences matter. A missed merge splits one person into several nodes and hides real links. A wrong merge fuses two people into one and invents links between their companies. The second is the more dangerous, and public data makes it easy: in the UK's company register, directors appointed after October 2015 show only a month and year of birth. So every merge in our graphs is a recorded decision with its evidence, reversible, and a finding that rests on one says so.

4. Provenance

An edge that cannot be traced to a record is an assertion. In a graph built from many sources this is easily lost: data is cleaned, deduplicated and reloaded, and by the end nobody can say which filing an edge came from.

We hold to one rule: every edge keeps a pointer to its record, meaning the register or document, the entry and the date we retrieved it. A path can then be shown, not just asserted: "Person X is linked to Company D in three steps" becomes three statements, each with a record a reader can open. When a source is corrected or withdrawn, the edges that depended on it can be found and removed. And two sources that disagree remain visible as a disagreement instead of one quietly overwriting the other.

5. Choosing the path

Ask a graph for the shortest path between two names and it will give you one, almost always through a hub, often through edges that never held on the same day. The shortest path is rarely the meaningful one. Three properties matter more than length:

• The kind of role. Shareholdings and board seats say more about control than a shared auditor or address.
• Recency and overlap. Steps that held at the same time, and recently, outweigh relations that ended decades apart.
• The rarity of the intermediaries. A path through someone on three boards says more than one through someone on three hundred.

Ranking paths this way turns a graph from a machine that connects everything into one that surfaces a short list worth checking. That list is where the work begins. Each path on it is still read record by record, with its dates, sources and ordinary explanations, before it becomes a finding.

In short

Most links in a graph of public records are true and uninformative. The few that matter are hidden by volume, not secrecy. Down-weighting hubs, dating every edge, treating identity as a recorded and reversible decision, tracing every edge to its source, and ranking paths by meaning rather than length: none of this is clever, and all of it is needed. Without it, a graph can make almost any two names look connected.