Nature normally hates power laws. In ordinary systems all quantities follow bell curves, and correlations decay rapidly, obeying exponential laws. But all that changes if the system is forced to undergo a phase transition. Then power laws emerge—nature’s unmistakable sign that chaos is departing in favor of order.

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. Sociologists would tell you that your subjects had just formed a community. Though

Most systems displaying a high degree of tolerance against failures share a common feature: Their functionality is guaranteed by a highly interconnected complex network. A cell’s robustness is hidden in its intricate

Putting the pieces of the puzzle together, we find that real networks are governed by two laws: growth and preferential attachment.

Despite their diversity most real networks share an essential feature: growth.

Clustering is indeed present in social systems.

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. Thus the power laws we spotted on the Web