Mathematical Continuity in Dynamic Social Networks

  • John L. Pfaltz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6984)


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.


Undirected Graph Closure Operator Neighborhood Closure Neighborhood System Continuous Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • John L. Pfaltz
    • 1
  1. 1.Dept. of Computer ScienceUniversity of VirginiaUSA

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