This model demonstrates the “connectivity avalanche” which occurs when edges are repeatedly added at random to link nodes in a graph. In 1959 Paul Erdos and AlfrÃˆd Renyi discovered that experiment the nodes suddenly all become linked into a single connected. In other words the network undergoes a phase change from essentially disconnected to connected.
This avalanche takes on great significance because networks are found in the patterns of connections that occur in virtually all systems (Green, 1994). For example, in a cellular automaton, the neighbourhood of each cell defines links to other cells that it interacts with. The result is that the connectivity avalanche is responsible for critical behaviour and phase changes in many kinds of systems. eg. crystallization, spread of epidemics, sand pile collapses, critical mass in nuclear chanin reactions.