Tree Decompositions and Social Graphs

TitleTree Decompositions and Social Graphs
Publication TypeTechnical Report
Year of Publication2014
AuthorsAdcock, A. B., Sullivan B. D., & Mahoney M. W.
Other Numbers3759

Recent work has established that large informatics graphs such as social and information networks have non-trivial tree-like structure when viewed at moderate size scales. Here, we present results from the first detailed empirical evaluation of the use of tree decomposition (TD) heuristics for structure identification and extraction in social graphs. Although TDs have historically been used in structural graph theory and scientific computing, we show that---even with existing TD heuristics developed for those very different areas---TD methods can identify interesting structure in a wide range of realistic informatics graphs. Among other things, we show that TD methods can identify structures that correlate strongly with the core-periphery structure of realistic networks, even when using simple greedy heuristics; we show that the peripheral bags of these TDs correlate well with low-conductance communities (when they exist) found using local spectral computations; and we show that several types of large-scale "ground-truth" communities, defined by demographic metadata on the nodes of the network, are well-localized in the large-scale and/or peripheral structures of the TDs. Our detailed empirical results for different TD heuristics on toy and synthetic networks help to establish a baseline to understand better the behavior of the heuristics on more complex real-world networks; and our results here suggest future directions for the development of improved TD heuristics that are more appropriate for improved structure identification in realistic networks.


We would like to acknowledge financial support from the Air Force Office of Scientific Research, the Army Research Office, the Defense Advanced Research Projects Agency, the National Consortium for Data Science, and the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of any of the above funding agencies.

Bibliographic Notes

Technical Report, Preprint: arXiv:1411.1546

Abbreviated Authors

A. B. Adcock, B. D. Sullivan, and M. W. Mahoney

ICSI Research Group

Big Data

ICSI Publication Type

Technical Report