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Degree distribution is a metric that tries to capture the difference in the degree of connectivity between nodes in a graph, it is essentially asking the question, do all the nodes have roughly the same amount of connections or do some have very many while others have very few connections? Degree distribution is an important metric in a network as it significantly contributes to the overall makeup of the system. A high degree distribution will likely mean a centralized network while a low degree distribution will mean a distributed network.