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In this article we provide a formal framework for reidentification in general. We define n-confusion as a concept for modeling the anonymity of a database table and we prove that n-confusion is a generalization of k-anonymity. After a short survey on the different available definitions of k-anonymity for graphs we provide a new definition for k-anonymous graph, which we consider to be the correct definition. We provide a description of the k-anonymous graphs, both for the regular and the non-regular case. We also introduce the more flexible concept of (k, l)-anonymous graph. Our definition of (k, l)-anonymous graph is meant to replace a previous definition of (k, l)-anonymous graph, which we here prove to have severe weaknesses. Finally, we provide a set of algorithms for k-anonymization of graphs. © 2012 Springer-Verlag.Partial  support  by  the  Spanish  MEC  projects ARES  (CONSOLIDER  INGENIO  2010  CSD2007-00004),  eAEGIS (TSI2007-65406-C03-02),  COPRIVACY  (TIN2011-27076-C03-03), and  RIPUP  (TIN2009-11689)  is  acknowledged.  One  author  is  partially supported by the FPU grant (BOEs 17/11/2009 and 11/10/2010) and by the Government of Catalonia under grant 2009 SGR 1135Peer Reviewe

Reidentification and k-anonymity: a model for disclosure risk in graphs