Now you would wonder whether it is feasible for nodes far apart to be talking to each other. The best part of this algorithm is that they do not need to! As long as there are a “sufficient” number of neighbours, the averaging of the estimated parameter happens, and one reaches convergence. An information theory like approach may be followed to obtain bounds!
The process is really simple and is closely related to Graph Theory. Consider 1 node (a sensor). At any time instant, all the neighbours of this node, broadcast their values to this node. This sensor at the next time iteration uses the data received from all its neighbours and its own previously sensed value to generate an estimate of the parameter.
It is very easy to show, that all the sensors converge to a value, which is equal to the average of the initial estimate in the ideal situation. But in practical cases we are faced with issues like limited bandwidth and power, failure of the communication system, possible introduction of directed graph (non-symmetric) which lead to faulty data transmissions. Its interesting to show whether in such real-life cases too these sensors reach convergence or do they fall apart as a bunch of squabbling pirates 😛