Abstract

Abstract
The problem of analyzing massive graph streams in real time is growing along with the size of streams. Sampling techniques have been used to analyze these streams in real time. However, it is difficult to answer questions like, which structures are well preserved by the sampling techniques over the evolution of streams? Which sampling techniques yield proper estimates for directed and weighted graphs? Which techniques have least time complexity etc? In this work, we have answered the above questions by comparing and analyzing the evolutionary samples of such graph streams. We have evaluated sequential sampling techniques by comparing the structural metrics from their samples. We have also presented a biased version of reservoir sampling, which shows better comparative results in our scenario. We have carried out rigorous experiments over a massive stream of 3 hundred million calls made by 11 million anonymous subscribers over 31 days. We evaluated node based and edge based methods of sampling. We have compared the samples generated by using sequential algorithms like, space saving algorithm for finding topK items, reservoir sampling, and a biased version of reservoir sampling. Our overall results and observations show that edge based samples perform well in our scenario. We have also compared the distribution of degrees and biases of evolutionary samples. © 2016 ACM.

Abstract

Abstract
With the realization of networks in many of the real world domains, research work in network science has gained much attention now-a-days. The real world interaction networks are exploited to gain insights into real world connections. One of the notion is to analyze how these networks grow and evolve. Most of the works rely upon the socio centric networks. The socio centric network comprises of several ego networks. How these ego networks evolve greatly influences the structure of network. In this work, we have analyzed the evolution of ego networks from a massive call network stream by using an extensive list of graph metrics. By doing this, we studied the evolution of structural properties of graph and related them with the real world user behaviors. We also proved the densification power law over the temporal call ego networks. Many of the evolving networks obey the densification power law and the number of edges increase as a function of time. Therefore, we discuss a sequential sampling method with forgetting factor to sample the evolving ego network stream. This method captures the most active and recent nodes from the network while preserving the tie strengths between them and maintaining the density of graph and decreasing redundancy.

Abstract

Abstract