Researchers have devoted themselves to exploring static features of social networks and further discovered many representative characteristics, such as power law in the degree distribution and assortative value used to differentiate social networks from nonsocial ones. However, people are not satisfied with these achievements and more and more attention has been paid on how to uncover those dynamic characteristics of social networks, especially how to track community evolution effectively. With these interests, in the paper we firstly display some basic but dynamic features of social networks. Then on its basis, we propose a novel core-based algorithm of tracking community evolution, CommTracker, which depends on core nodes to establish the evolving relationships among communities at different snapshots. With the algorithm, we discover two unique phenomena in social networks and further propose two representative coefficients: GROWTH and METABOLISM by which we are also able to distinguish social networks from nonsocial ones from the dynamic aspect. At last, we have developed a social network model which has the capabilities of exhibiting two necessary features above.
As forerunners, A.L.Barabasi and H.Jeong study static characteristic variations on the network of scientific collaboration @cite_15 . Gergely Palla and A.-L. Barabasi provide a method which effectively utilizes edge overlapping to build evolving relationship @cite_4 . With the approach, they discover valuable phenomena of social community evolution.
@cite_15 @cite_4
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We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We investigate phase transitions in graph structure as the relative weighting of these two components of the attachment rule is varied. Previous work of one of the authors showed that when the geometric component is weak, the limiting degree sequence of the resulting graph coincides with that of the standard Barab 'asi--Albert preferential attachment model. We show that at the other extreme, in the case of a sufficiently strong geometric component, the limiting degree sequence coincides with that of a purely geometric model, the on-line nearest-neighbour graph, which is of interest in its own right and for which we prove some extensions of known results. We also show the presence of an intermediate regime, in which the behaviour differs significantly from both the on-line nearest-neighbour graph and the Barab 'asi--Albert model; in this regime, we obtain a stretched exponential upper bound on the degree sequence. Our results lend some mathematical support to simulation studies of Manna and Sen, while proving that the power law to stretched exponential phase transition occurs at a different point from the one conjectured by those authors. The co-authorship network of scientists represents a prototype of complex evolving networks. In addition, it offers one of the most extensive database to date on social networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an 8-year period (1991–98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. Three complementary approaches allow us to obtain a detailed characterization. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, affecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the network's time evolution. In some limits the model can be solved analytically, predicting a two-regime scaling in agreement with the measurements. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically. The combined numerical and analytical results underline the important role internal links play in determining the observed scaling behavior and network topology. The results and methodologies developed in the context of the co-authorship network could be useful for a systematic study of other complex evolving networks as well, such as the world wide web, Internet, or other social networks. It has long been realized that social network of scientific collaborations provides a window on patterns of collaboration within the academic community. Investigations and studies about static and dynamic properties of co-authorship network have also been done in the recent years. However, the accent of most of the research is on the analysis about the macroscopic structure of the whole network or community over time such as distance, diameter shrinking and densication phenomenon and microscopic formation analysis of links,groups or communities over time. But in fact, how an individual or a community grows over time may not only provide a new view point to mine copious and valuable information about scientific networks but also reveal important factors that influence the growth process. In this paper,from a temporal and microscopic analytical perspective, we propose a method to trace scientific individual's and community's growth process based on community's evolution path combination with quantifiable measurements. During the process of tracing, we find out that it is the fact that the lifespan of community is related to the ability of altering its membership, but what's more and complementary, we find out that the lifespan of community is also related to the ability of maintaining its core members meaning that community may last for a longer lifespan if its core members are much more stable. Meanwhile, we also trace the growth process of research individuals based on the evolution of communities. Research on performance, robustness, and evolution of the global Internet is fundamentally handicapped without accurate and thorough knowledge of the nature and structure of the contractual relationships between Autonomous Systems (ASs). In this work we introduce novel heuristics for inferring AS relationships. Our heuristics improve upon previous works in several technical aspects, which we outline in detail and demonstrate with several examples. Seeking to increase the value and reliability of our inference results, we then focus on validation of inferred AS relationships. We perform a survey with ASs' network administrators to collect information on the actual connectivity and policies of the surveyed ASs. Based on the survey results, we find that our new AS relationship inference techniques achieve high levels of accuracy: we correctly infer 96.5 customer to provider (c2p), 82.8 peer to peer (p2p), and 90.3 sibling to sibling (s2s) relationships. We then cross-compare the reported AS connectivity with the AS connectivity data contained in BGP tables. We find that BGP tables miss up to 86.2 of the true adjacencies of the surveyed ASs. The majority of the missing links are of the p2p type, which highlights the limitations of present measuring techniques to capture links of this type. Finally, to make our results easily accessible and practically useful for the community, we open an AS relationship repository where we archive, on a weekly basis, and make publicly available the complete Internet AS-level topology annotated with AS relationship information for every pair of AS neighbors.