Mathematicians call this phenomenon the emergence of a giant component, one that includes a large fraction of all nodes. Physicists call it percolation and will tell you that we just witnessed a phase transition, similar to the moment in which water freezes.
What is the structure of the network encoding how the crickets, or people influence each other?
Power laws rarely emerge in systems completely dominated by a roll of the dice. Physicists have learned that most often they signal a transition from disorder to order.
Trapped between order and chaos, water molecules participate in a majestic dance in which some molecules come together, form small and somewhat ordered groups, move together, and in no time break apart to join other molecules forming yet other groups.
In the vicinity of the critical point we need to stop viewing atoms separately.
The theory of phase transition told us loud and clear that the road from disorder to order is maintained by the powerful forces of self-organization.
Errors and failures typically corrupt all human designs.
Computer simulations we performed on networks generated by the scale-free model indicated that a significant fraction of nodes can be randomly removed from any scale-free network without its breaking apart.
Innovations spread from innovators to hubs.
We need to understand living systems in their integrity.
Real networks are not static, as all graph theoretical models were until recently. Instead, growth plays a key role in shaping their topology.