  Models of complex networks are generally defined as graph stochastic
processes in which edges and vertices are added or deleted over time to
simulate the evolution of networks. Here, we define a unifying framework -
probabilistic inductive classes of graphs - for formalizing and studying
evolution of complex networks. Our definition of probabilistic inductive class
of graphs (PICG) extends the standard notion of inductive class of graphs (ICG)
by imposing a probability space. A PICG is given by: (1) class B of initial
graphs, the basis of PICG, (2) class R of generating rules, each with
distinguished left element to which the rule is applied to obtain the right
element, (3) probability distribution specifying how the initial graph is
chosen from class B, (4) probability distribution specifying how the rules from
class R are applied, and, finally, (5) probability distribution specifying how
the left elements for every rule in class R are chosen. We point out that many
of the existing models of growing networks can be cast as PICGs. We present how
the well known model of growing networks - the preferential attachment model -
can be studied as PICG. As an illustration we present results regarding the
size, order, and degree sequence for PICG models of connected and 2-connected
graphs.
