Abstract This paper reports on stable (or invariant) properties of human interaction networks, with benchmarks derived from public email lists. Activity, recognized through messages sent, along time and topology were observed in snapshots in a timeline, and at different scales. Our analysis shows that activity is practically the same for all networks across timescales ranging from seconds to months. The principal components of the participants in the topological metrics space remain practically unchanged as different sets of messages are considered. The activity of participants follows the expected scale-free trace, thus yielding the hub, intermediary and peripheral classes of vertices by comparison against the Erdos–Renyi model. The relative sizes of these three sectors are essentially the same for all email lists and the same along time. Typically, 15 of the vertices are hubs, 15 –45 are intermediary and > 45 are peripheral vertices. Similar results for the distribution of participants in the three sectors and for the relative importance of the topological metrics were obtained for 12 additional networks from Facebook, Twitter and ParticipaBR. These properties are consistent with the literature and may be general for human interaction networks, which has important implications for establishing a typology of participants based on quantitative criteria.
Research on network evolution is often restricted to network growth, in which there is a monotonic increase in the number of events @cite_16 . Exceptions are reported in this section, with emphasis on those more closely related to the present article.
@cite_16
1990271487 2151078464 2082986408 2136931666
Motivated by data on the evolution of the Internet and World Wide Web we consider scenarios of self-organization of the nonlinearly growing networks into free-scale structures. We find that the accelerating growth of the networks establishes their structure. For the growing networks with preferential linking and increasing density of links, two scenarios are possible. In one of them, the value of the exponent @math of the connectivity distribution is between 3 2 and 2. In the other, @math and the distribution is necessarily non-stationary. We present a detailed study of network evolution by analyzing four large online social networks with full temporal information about node and edge arrivals. For the first time at such a large scale, we study individual node arrival and edge creation processes that collectively lead to macroscopic properties of networks. Using a methodology based on the maximum-likelihood principle, we investigate a wide variety of network formation strategies, and show that edge locality plays a critical role in evolution of networks. Our findings supplement earlier network models based on the inherently non-local preferential attachment. Based on our observations, we develop a complete model of network evolution, where nodes arrive at a prespecified rate and select their lifetimes. Each node then independently initiates edges according to a "gap" process, selecting a destination for each edge according to a simple triangle-closing model free of any parameters. We show analytically that the combination of the gap distribution with the node lifetime leads to a power law out-degree distribution that accurately reflects the true network in all four cases. Finally, we give model parameter settings that allow automatic evolution and generation of realistic synthetic networks of arbitrary scale. Based on the empirical analysis of the dependency network in 18 Java projects, we develop a novel model of network growth which considersboth: an attachment mechanism and the addition of new nodes with a heterogeneous distribution of their initial degree, k0. Empirically we find that the cumulative degree distributions of initial degrees and of the final network, follow power-law behaviors: P(k0) ∝ k01−α, and P(k) ∝ k1−γ, respectively. For the total number of links as a function of the network size, we find empirically K(N) ∝ Nβ, where β is (at the beginning of thenetwork evolution) between 1.25 and 2, while converging to ∼ 1 for large N. This indicates a transition from a growth regime with increasing network density towards a sustainable regime, which revents a collapse because of ever increasing dependencies. Our theoretical framework is able to predict relations between the exponents α, β, γ, which also link issues of software engineering and developer activity. These relations are verified by means of computer simulations and empirical investigations. They indicate that the growth of real Open Source Software networks occurs on the edge between two regimes, which are either dominated by the initial degree distribution of added nodes, or by the preferential attachment mechanism. Hence, the heterogeneous degree distribution of newly added nodes, found empirically, is essential to describe the laws of sustainable growth in networks. We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrat...