Mathematical Continuity in Dynamic Social Networks

A rigorous concept of continuity for dynamic networks is developed. It is based on closed, rather than open, sets. It is local in nature, in that if the network change is discontinuous it will be so at a single point and the discontinuity will be apparent in that point’s immediate neighborhood. Necessary and sufficient criteria for continuity are provided when the change involves only the addition or deletion of individual nodes or connections (edges). Finally, we show that an effective network process to reduce large networks to their fundamental cycles is continuous.

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