I am analyzing social networks (not virtual) and I am observing the connections between people. If a person would choose another person to connect with randomly, the number of connections within a group of people would be distributed normally - at least according to the book I am currently reading.
How can we know the distribution is Gaussian (normal)? There are other distributions such as Poisson, Rice, Rayliegh, etc. The problem with the Gaussian distribution in theory is that the values go from $-\infty$ to $+\infty$ (although the probabilities go toward zero) and the number of connections cannot be negative.
Does anyone know which distribution can be expected in case each person independently (randomly) picks-up another person to connect with?