We introduce an approach for the quantitative assessment of the connectivity in neuronal cultures, based on the statistical mechanics of percolation on a graph. This allows us to monitor the development of the culture and to see the emergence of connectivity in the network. The culture becomes fully connected at a time equivalent to the expected time of birth. The spontaneous bursting activity that characterizes cultures develops in parallel with the connectivity. The average number of inputs per neuron can be quantitatively determined in units of m(0), the number of activated inputs needed to excite the neuron. For m(0) approximately 15 we find that hippocampal neurons have on average approximately 60-120 inputs, whereas cortical neurons have approximately 75-150, depending on neuronal density. The ratio of excitatory to inhibitory neurons is determined by using the GABA(A) antagonist bicuculine. This ratio changes during development and reaches the final value at day 7-8, coinciding with the expected time of the GABA switch. For hippocampal cultures the inhibitory cells comprise approximately 30% of the neurons in the culture whereas for cortical cultures they are approximately 20%. Such detailed global information on the connectivity of networks in neuronal cultures is at present inaccessible by any electrophysiological or other technique.