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We consider the problems of computing the average degree and the size of agiven network in a distributed fashion under quantized communication. Wepresent two distributed algorithms which rely on quantized operation (i.e.,nodes process and transmit quantized messages), and are able to calculate theexact solutions in a finite number of steps. Furthermore, during the operationof our algorithms, each node is able to determine in a distributed mannerwhether convergence has been achieved and thus terminate its operation. To thebest of the authors' knowledge these algorithms are the first to find the exactsolutions under quantized communication (i.e., there is no error in the finalcalculation). Additionally, note that our network size calculation algorithm isthe first in the literature which calculates the exact size of a network in afinite number of steps without introducing a final error. This error in otheralgorithms can be either due to quantization or asymptotic convergence. In ourcase, no error is introduced since the desired result is calculated in the formof a fraction involving a quantized numerator and a quantized denominator.Finally, we demonstrate the operation of our algorithms and their potentialadvantages.

Distributed Computation of Exact Average Degree and Network Size in Finite Number of Steps under Quantized Communication