Can power law distribution be used to explain emergent properties?

In a normal distribution the behaviour, or properties, of the system can be predicted by the average of the components. In a power law or scale free distribution, there is no average and super nodes 'emerge' from the interconnections formed through growth, preferential attachment and fitness as the system changes over time - is this the same as emergent properties?

I know everyone is busy at the moment, but I'd really appreciate any thoughts on this.

Thanks