Directed networks’ different link formation mechanisms causing degree distribution distinction

Within undirected networks, scientists have shown much interest in presenting power-law features. For instance, Barabási and Albert (1999) claimed that a common property of many large networks is that vertex connectivity follows scale-free power-law distribution, and in another study Barabási et al. (2002) showed power law evolution in the social network of scientific collaboration. At the same time, Jiang et al. (2011) discussed deviation from power-law distribution; others indicated that size effect (Bagrow et al., 2008), information filtering mechanism (Mossa et al., 2002), and birth and death process (Shi et al., 2005) could account for this deviation. Within directed networks, many authors have considered that outlinks follow a similar mechanism of creation as inlinks’ (Faloutsos et al., 1999; Krapivsky et al., 2001; Tanimoto, 2009) with link creation rate being the linear function of node degree, resulting in a power-law shape for both indegree and outdegree distribution. Some other authors have made an assumption that directed networks, such as scientific collaboration or citation, behave as undirected, resulting in a power-law degree distribution accordingly (Barabási et al., 2002). At the same time, we claim (1) Outlinks feature different degree distributions than inlinks; where different link formation mechanisms cause the distribution distinctions, (2) in/outdegree distribution distinction holds for different levels of system decomposition; therefore this distribution distinction is a property of directed networks. First, we emphasize in/outlink formation mechanisms as causal factors for distinction between indegree and outdegree distributions (where this distinction has already been noticed in Barker et al. (2010) and Baxter et al. (2006)) within a sample network of OSS projects as well as Java software corpus as a network. Second, we analyze whether this distribution distinction holds for different levels of system decomposition: open-source-software (OSS) project–project dependency within a cluster, package–package dependency within a project and class–class dependency within a package. We conclude that indegree and outdegree dependencies do not lead to similar type of degree distributions, implying that indegree dependencies follow overall power-law distribution (or power-law with flat-top or exponential cut-off in some cases), while outdegree dependencies do not follow heavy-tailed distribution.