Stability of graph communities across time scales

Details Stability of graph communities across time scales Stability of graph communities across time scales

2008-12-09

arxiv.org/abs/0812.1811v4

Physics

Physics and Society

submitted; updated bibliography from v3

Scientific paper

The complexity of biological, social and engineering networks makes it desirable to find natural partitions into communities that can act as simplified descriptions and provide insight into the structure and function of the overall system. Although community detection methods abound, there is a lack of consensus on how to quantify and rank the quality of partitions. We show here that the quality of a partition can be measured in terms of its stability, defined in terms of the clustered autocovariance of a Markov process taking place on the graph. Because the stability has an intrinsic dependence on time scales of the graph, it allows us to compare and rank partitions at each time and also to establish the time spans over which partitions are optimal. Hence the Markov time acts effectively as an intrinsic resolution parameter that establishes a hierarchy of increasingly coarser clusterings. Within our framework we can then provide a unifying view of several standard partitioning measures: modularity and normalized cut size can be interpreted as one-step time measures, whereas Fiedler's spectral clustering emerges at long times. We apply our method to characterize the relevance and persistence of partitions over time for constructive and real networks, including hierarchical graphs and social networks. We also obtain reduced descriptions for atomic level protein structures over different time scales.

Affiliated with

Also associated with

No associations

Rating

Stability of graph communities across time scales does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Stability of graph communities across time scales, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stability of graph communities across time scales will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-526814