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Probabilistic analysis of distinctive features for discovering growth mechanism in complex networks

Zhuang, Di (2021) Probabilistic analysis of distinctive features for discovering growth mechanism in complex networks.

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Abstract:Scale-free networks are networks that have power-law degree distribution, at least asymptotically. They are important in complex network theory because many real-world networks are found to be scale-free. In complex network theory, preferential attachment (PA) and fitness (F) are two hypothetical mechanisms that drive the evolution of scale-free networks. Although both of them are able to generate scale-free networks, they are different with respect to the temporal changes they produce during the development of the networks, which might have implications for the future structure of the networks. Therefore, how to discover the growth mechanisms behind a network becomes important. The goal of this work is to do mathematical analysis on distinctive features for discovering growth mechanisms in complex networks. We propose an F-based model with exponentially distributed fitness value and show empirically that it is able to generate scale-free networks for certain parameter values. In addition, we analyze a PA-based model and the F-based model and show that they are different under certain conditions. In particular, we show that the expected value of the distinctive feature - the average number of new links that a group of nodes receives during a certain time interval after normalization - of the PA-based model is strictly greater than that of the F-based model. Note that this article is part of a larger project that aims to develop a classifier that, given a synthetic network, is able to tell which mechanism from PA and F fits the network the best. The analytical results in this work will be compared to the empirical results obtained in Weiting Cai’s work [3] of developing the machine-learning classifier.
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics BSc (56965)
Link to this item:http://purl.utwente.nl/essays/86679
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