Bell curve ignores deviations and creates a description of reality that doesn't take any exclusions into account (that can in fact radically transform it). So random networks are the ones where the possibility of a rare connected node is quite high and in fact defines the properties of the network.

the large k-tail (probability with the increasing number of attempts) of power law decays much more slowly than the tail of the Poissonian, so there are a small but significant number of vertices in the network with very high degree.

poissonian distribution can be used to see if a sequence of events were generated by a random process. if distribution of event probabilities approximates towards poisson distribution p(k) = (m^k * e^-m)/k! then these events were most probably generated by a random process. (m ­ mean number of events in a time... [Read All]

if web were a random (directed) graph then the degree distributions would take the simple Poissonian form

poisson models the number of events with fixed intervals, while binominal models the individual events.

for example, if car speed is a random variable, one can use binominal/normal distribution to model variation in individual car speeds, and poisson distribution to model the number of cars that pass a certain point... [Read All]