Abstract
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.
Highlights
Q3Among network models Erdős–Rényi (ER) [1] proposed a non-growing randomly connected model, Watts and Strogatz (WS) [2] proposed a non-growing randomly re-connected network model and Barabási–Albert (BA) [3] proposed a growing network with the probability of addition of new nodes proportional to the number of incoming links
We argue that WWW, Scientific Collaboration and OSS reuse networks are not undirected, as assumed in some studies; they are directed networks where outlinks and inlinks demonstrate different degree distributions
We claim that there are different inlink formation mechanisms within directed networks which result in degree distribution distinctions
Summary
Among network models Erdős–Rényi (ER) [1] proposed a non-growing randomly connected model, Watts and Strogatz (WS) [2] proposed a non-growing randomly re-connected network model (so called small world) and Barabási–Albert (BA) [3] proposed a growing network with the probability of addition of new nodes proportional to the number of incoming links (so-called preferential attachment model or rich-get-richer). Preferential attachment does not always explain network evolution, e.g. where the innovation of an article rather than the number of its citations causes a new attachment Scientists such as Ergun et al [9] and Xu et al [10] have discussed a methodology of fit-get-richer, implying that new vertices connect to highly fitted vertices. Faloutsos et al [17] showed power-law features existing in the internet topology, implying its benefits in designing efficient protocols, creating accurate artificial models and speculating on the internet topology in the future. Faloutsos et al [17], Krapivsky et al [24], Tanimoto [25] and more assumed that preferential attachment is the dominant link formation mechanism in directed networks, resulting in power-law degree distribution. We first consider the sample network of open-source-software (OSS) projects reuse to identify the distinction between indegree and outdegree distribution, analyze whether this distinction holds in the corpus of each of those OSS projects, and at different system decomposition levels of package–package and class–class dependencies
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physica A: Statistical Mechanics and its Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
