• Critical percolation on random regular graphs 

      Joos, Felix; Perarnau Llobet, Guillem (2018-03-20)
      Article
      Accés obert
      We show that for all $ d\in \{3,\ldots ,n-1\}$ the size of the largest component of a random $ d$-regular graph on $ n$ vertices around the percolation threshold $ p=1/(d-1)$ is $ \Theta (n^{2/3})$, with high probability. ...
    • How to determine if a random graph with a fixed degree sequence has a giant component 

      Joos, Felix; Perarnau Llobet, Guillem; Rautenbach, Dieter; Reed, Bruce (2017-01-26)
      Article
      Accés obert
      For a fixed degree sequence D=(d1,…,dn) , let G(D) be a uniformly chosen (simple) graph on {1,…,n} where the vertex i has degree di . In this paper we determine whether G(D) has a giant component with high probability, ...
    • How to determine if a random graph with a fixed degree sequence has a giant component 

      Joos, Felix; Perarnau Llobet, Guillem; Rautenbach, Dieter; Reed, Bruce (Institute of Electrical and Electronics Engineers (IEEE), 2016)
      Text en actes de congrés
      Accés obert
      The traditional Erdos-Renyi model of a random network is of little use in modelling the type of complex networks which modern researchers study. In this graph, every pair of vertices is equally likely to be connected by ...
    • Percolation on random graphs with a fixed degree sequence 

      Fountoulakis, Nikolaos; Joos, Felix; Perarnau Llobet, Guillem (2022-01-04)
      Article
      Accés obert
      We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We ...