  Our work introduces an approach for estimating the contribution of attachment
mechanisms to the formation of growing networks. We present a generic model in
which growth is driven by the continuous attachment of new nodes according to
random and preferential linkage with a fixed probability. Past approaches apply
likelihood analysis to estimate the probability of occurrence of each mechanism
at a particular network instance, exploiting the concavity of the likelihood
function at each point in time. However, the probability of connecting to
existing nodes, and consequently the likelihood function itself, varies as
networks grow. We establish conditions under which applying likelihood analysis
guarantees the existence of a local maximum of the time-varying likelihood
function and prove that an expectation maximization algorithm provides a
convergent estimate. Furthermore, the in-degree distributions of the nodes in
the growing networks are analytically characterized. Simulations show that,
under the proposed conditions, expectation maximization and maximum-likelihood
accurately estimate the actual contribution of each mechanism, and in-degree
distributions converge to stationary distributions.
