Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Graph evolution: Densification and shrinking diameters
ACM Transactions on Knowledge Discovery from Data (TKDD)
Scalable modeling of real graphs using Kronecker multiplication
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COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Realistic, mathematically tractable graph generation and evolution, using kronecker multiplication
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
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On the privacy of anonymized networks
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During the past decade, a number of different studies have identified several peculiar properties of networks that arise from a diverse universe, ranging from social to computer networks. A recently observed feature is known as network densification, which occurs when the number of edges grows much faster than the number of nodes, as the network evolves over time. This surprising phenomenon has been empirically validated in a variety of networks that emerge in the real world and mathematical models have been recently proposed to explain it. Leveraging on how real data is usually gathered and used, we propose a new model called Edge Sampling to explain how densification can arise. Our model is innovative, as we consider a fixed underlying graph and a process that discovers this graph by probabilistically sampling its edges. We show that this model possesses several interesting features, in particular, that edges and nodes discovered can exhibit densification. Moreover, when the node degree of the fixed underlying graph follows a heavy-tailed distribution, we show that the Edge Sampling model can yield power law densification, establishing an approximate relationship between the degree exponent and the densification exponent. The theoretical findings are supported by numerical evaluations of the model. Finally, we apply our model to real network data to evaluate its performance on capturing the previously observed densification. Our results indicate that edge sampling is indeed a plausible alternative explanation for the densification phenomenon that has been recently observed.