The graph is built from what you publish and what corroborates it. Structured data declares the claims; profiles, registrations and citations elsewhere either support them or leave them dangling.
Consistency is the whole discipline. The same name, the same address, the same founding date, the same service descriptions, everywhere. A detail that differs between your own pages is a contradiction the engine has to resolve, usually by trusting less of it.
And nothing should be asserted that cannot be corroborated. A founder node pointing at a person who resolves nowhere is a claim a system has to discount, which is worse than having no founder node at all.
What strengthens an entity graph?
Consistent structured data across every page, details that match everywhere they appear, and external profiles or registrations that corroborate the claims rather than merely repeating them.
Should you assert everything you can?
No. An assertion that resolves nowhere gets discounted and drags the credibility of the rest with it. Absent beats unverifiable.