Network growth algorithms

Growth processes are a fundamentally different approach compared to probability-driven exponential models covered in earlier chapters. This chapter studies how growth rules can be designed to mimic processes observed in the real world, and how the process can be mathematically analyzed in order to obtain information about the likely topological properties of the resulting networks. The configuration (stub joining) model is described, including a careful discussion of how bias can be introduced if backtracking is used instead of restarting if stubs join to form a self or double link. The second class of models looked at is preferential attachment. The simplest variants of this are analyzed with a master equation approach, in order to introduce this technique as a way of obtaining analytical information about the expected properties of the generated graphs. Extensive references are provided to the numerous variants and extensions of both of these models.