The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two independent pure birth processes that are observed at a common exponentially distributed time T (thus creating dependence between in- and out-degree). The characterization gives an explicit form for the joint degree distribution, and this confirms previously derived tail probabilities for the two marginal degree distributions. The new characterization is also used to obtain an explicit expression for tail probabilities in which both degrees are large. A new generalized directed preferential attachment model is then defined and analyzed using similar methods. The two extensions, motivated by empirical evidence, are to allow double-directed (i.e. undirected) edges in the network, and to allow the probability of connecting an ingoing (outgoing) edge to a specified node to also depend on the out-degree (in-degree) of that node.

The clustering coefficient is typically used as a measure of the prevalence of node clusters in a network. Various definitions for this measure have been proposed for the cases of networks having weighted edges which may or not be directed. However, these techniques consistently assume that only a subset of all possible edges is present in the network, whereas there are weighted networks of interest in which all possible edges are present, that is, complete weighted networks. For this situation, the concept of clustering is redefined, and computational techniques are presented for computing an associated clustering coefficient for complete weighted undirected or directed networks. The performance of this new definition is compared with that of current clustering definitions when extended to complete weighted networks.