> Thinking back, it is true that most of my very seemingly random leads came from people who were weakly connected with me and they would be considered equals.

For anyone else reading (sounds like the OP might already be aware), you may enjoy "The Strength of Weak Ties" by Mark Granovetter, a legendary paper in the field of network science, which describes exactly this phenomenon.

https://www.cs.cmu.edu/~jure/pub/papers/granovetter73ties.pd...