A team's social fabric is a summation of the number of conversations that the team has together. The social fabric is the quantum and quality of the social bonds that exist amongst a group of people. The higher the social fabric, the higher the trust, and the lowering of the friction for a group to achieve a goal.
Good social fabric is largely dictated by the quantity of conversations. In many ways, the quality of the conversations is irrelevant, as long as it is sufficient. There must be some shared values or quality as a baseline.
The quantity of total conversations (in number) is much more important than the quantity of each conversation (in time). Five conversations over a week of 15 minutes each is much more important than one conversation of 75 minutes. The reason is that that there are diminishing returns to a long conversation; after time, people tune out to what is being said out of short attention spans.
The metric for good social fabric is dependent on that quantity, more than anything else. A quick measure is how many conversations happened along a span of time (velocity) with how many people (reach). One metric may be to divide the number of conversations (velocity) over time, with a weighting assigned to the number of people.