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In a peer-to-peer (P2P) network, a 'fabric' of overlay links helps peers discover and use other peers' resources. This fabric, however, is highly dynamic and constantly changing. While different measures of dynamicity have been implicitly and explicitly proposed, there is lack of deeper understanding about the various aspects of dynamicity. We systematically evaluate and quantify different dimensions of dynamicity through controlled generation of different dynamic networks. We also introduce a new dimension of dynamicity, persistence, which quantifies stable nodes in a network. This measure could be quite useful in the design and testing of P2P protocols that exploit the presence of stable nodes. Also, quite coincidentally, and to our surprise, a certain type of dynamic network that we designed has node degree properties that resemble those observed in social networks.