link privacy between labeled vertics

　　　　There  are  two  main  mechnisms  for preserving   link privacy between labeled vertices. The  first  approach  is  to perform  clustering of vertices  and  edges,and  aggregate them into super vertices.in  this  way,information about corresponding sub-graphs can be anonymized.While  these  clustering approaches permit analysis of some  macro-level graph properties,they  are  not suitable for  blackbox application   of  existing  social  network   based  applications.such as  sybil defenses.The second class of approaches  aim to introduce perturbation in  the social graph by  adding  and  deleting edges  and  vertices.Next  ,we discuss this  line of  research  in  more  detail.

　　　　Hay  propose a perturbation algorithm which  applies a  sequences of  K   edge  deletions   followed  by  k random edge  insertions.Candidates  for  edge deletion  are  sampled uniformly at  random  from  the  space of  existing  edges  in  graph  G,while  candidates for edge insertion are  sampled uniformly  at  random from the space of  edges not  in  G.The key difference between our perturbation  mechanism and  that  of  Hay  is  that  we  sample  edges for insetion based on the structure of  the  original  graph(as  opposed to random selection).