Your comments

Ok, but I cannot do it from the model details screen. Should I open heavy diagram screen only to share the model?

This is misleading.

However, it seems to be related to dragging columns in view definition. After crash the column that was being dragged at time of crash is named column_(number) and it is on its original position.

This might be related to reverse engineering somehow, because the model was initially exported from Oracle to Vertabelo XML and imported back as PostgreSQL.

Thanks for your response. Shouldn't new visual representations have this checked by default? It seems hard to guess.
No, I was looking for a method to make diagram look acceptable automatically.

For example, when I select 5 related tables, and then ask Vertabelo to layout them. It should place tables so that the graph would be possibly planar and with possibly short reference links. It could also follow Dead Crows Fly East principle.

This is certainly not a crucial feature. However, it would make working with reverse-engineered models easier.
Ok, so as for now it is not possible to hide references.

Can I move a single reference to be connected to another instance of the same table in the diagram?