forest.fire.game           package:igraph           R Documentation

_F_o_r_e_s_t _F_i_r_e _N_e_t_w_o_r_k _M_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

     This is a growing network model, which resembles of how the forest
     fire spreads by igniting trees close by.

_U_s_a_g_e:

     forest.fire.game (nodes, fw.prob, bw.factor = 1, ambs = 1, directed = TRUE, 
         verbose = igraph.par("verbose")) 

_A_r_g_u_m_e_n_t_s:

   nodes: The number of vertices in the graph.

 fw.prob: The forward burning probability, see details below.

bw.factor: The backward burning ratio. The backward burning probability
          is calculated as 'bw.factor*fw.prob'.

    ambs: The number of ambassador vertices.

directed: Logical scalar, whether to create a directed graph.

 verbose: Logical scalar, whether to "draw" a progress bar.

_D_e_t_a_i_l_s:

     The forest fire model intends to reproduce the following network
     characteristics, observed in real networks:

        *  Heavy-tailed in-degree distribution. 

        *  Heavy-tailed out-degree distribution.

        *  Communities.

        *  Densification power-law. The network is densifying in time,
           according to a power-law rule.

        *  Shrinking diameter. The diameter of the network decreases in
           time.

     The network is generated in the following way. One vertex is added
     at a time. This vertex connects to (cites) 'ambs' vertices already
     present in the network, chosen uniformly random. Now, for each
     cited vertex v we do the following procedure:

        1.  We generate two random number, x and y, that are
           geometrically distributed with means p/(1-p) and rp(1-rp).
           (p is 'fw.prob', r is 'bw.factor'.) The new vertex cites x
           outgoing neighbors and y incoming neighbors of v, from those
           which are not yet cited by the new vertex. If there are less
           than x or y such vertices available then we cite all of
           them.

        2.  The same procedure is applied to all the newly cited
           vertices.

_V_a_l_u_e:

     A simple graph, possibly directed if the 'directed' argument is
     'TRUE'.

_N_o_t_e:

     The version of the model in the published paper is incorrect in
     the sense that it cannot generate the kind of graphs the authors
     claim. A corrected version is available from <URL:
     http://www.cs.cmu.edu/~jure/pubs/powergrowth-tkdd.pdf>, our
     implementation is based on this.

_A_u_t_h_o_r(_s):

     Gabor Csardi csardi@rmki.kfki.hu

_R_e_f_e_r_e_n_c_e_s:

     Jure Leskovec, Jon Kleinberg and Christos Faloutsos. Graphs over
     time: densification laws, shrinking diameters and possible
     explanations. _KDD '05: Proceeding of the eleventh ACM SIGKDD
     international conference on Knowledge discovery in data mining_,
     177-187, 2005.

_S_e_e _A_l_s_o:

     'barabasi.game' for the basic preferential attachment model.

_E_x_a_m_p_l_e_s:

     g <- forest.fire.game(10000, fw.prob=0.37, bw.factor=0.32/0.37)
     dd1 <- degree.distribution(g, mode="in")
     dd2 <- degree.distribution(g, mode="out")
     if (interactive()) {
       plot(seq(along=dd1)-1, dd1, log="xy")
       points(seq(along=dd2)-1, dd2, col=2, pch=2)
     }

