New topologies from old via ideals
American Mathematical Monthly
Discrete Mathematics
Graph Theory: Modeling, Applications, and Algorithms
Graph Theory: Modeling, Applications, and Algorithms
Statistical properties of community structure in large social and information networks
Proceedings of the 17th international conference on World Wide Web
Detecting Structural Changes and Command Hierarchies in Dynamic Social Networks
ASONAM '09 Proceedings of the 2009 International Conference on Advances in Social Network Analysis and Mining
Finding the Mule in the Network
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
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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.