Knowledge and Information Systems

, Volume 45, Issue 3, pp 645–678 | Cite as

Estimating robustness in large social graphs

  • Fragkiskos D. Malliaros
  • Vasileios Megalooikonomou
  • Christos Faloutsos
Regular Paper


Given a large social graph, what can we say about its robustness? Broadly speaking, the property of robustness is crucial in real graphs, since it is related to the structural behavior of graphs to retain their connectivity properties after losing a portion of their edges/nodes. Can we estimate a robustness index for a graph quickly? Additionally, if the graph evolves over time, how this property changes? In this work, we are trying to answer the above questions studying the expansion properties of large social graphs. First, we present a measure that characterizes the robustness properties of a graph and also serves as global measure of the community structure (or lack thereof). We show how to compute this measure efficiently by exploiting the special spectral properties of real-world networks. We apply our method on several diverse real networks with millions of nodes, and we observe interesting properties for both static and time-evolving social graphs. As an application example, we show how to spot outliers and anomalies in graphs over time. Finally, we examine how graph generating models that mimic several properties of real-world graphs and behave in terms of robustness dynamics.


Network robustness Expansion properties Temporal evolution Graph generating models Social network analysis  Graph mining 



Fragkiskos D. Malliaros is a recipient of the Google Europe Fellowship in Graph Mining, and this research is supported in part by this Google Fellowship. Vasileios Megalooikonomou is partially supported by the ARMOR Project (FP7-ICT-2011-5.1-287720) that is co-funded by the European Commission under the Seventh Framework Programme and by the European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the NSRF—Research Funding Program: Thales. Investing in knowledge society through the European Social Fund. Christos Faloutsos is supported by the National Science Foundation under Grants No. IIS-1217559 CNS-1314632, by the Army Research Laboratory under Cooperative Agreement Number W911NF-09-2-0053 and under Contract Number W911NF-11-C-0088, by an IBM Faculty Award and a Google Focused Research Award. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation, or other funding parties. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.


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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Fragkiskos D. Malliaros
    • 1
    • 5
  • Vasileios Megalooikonomou
    • 2
    • 3
  • Christos Faloutsos
    • 4
  1. 1.Computer Science LaboratoryÉcole PolytechniquePalaiseauFrance
  2. 2.Department of Computer Engineering and InformaticsUniversity of PatrasRioGreece
  3. 3.Center for Data Analytics and Biomedical InformaticsTemple UniversityPhiladelphiaUSA
  4. 4.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA
  5. 5.Laboratoire d’Informatique (LIX)PalaiseauFrance

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