Abstract
Abstract Graph datasets are common in many application domains and for which their graphs are usually massive. One solution to process such massive graphs is summarization. There are two kinds of graphs, stationary and stream. For stationary graphs, a number of summarization algorithms are available while for graph stream there is no a comprehensive summarization method that summarizes a graph stream based on the structure, vertex attributes or both with varying contributions. This is because of challenges of graph stream, which are volume of data and changing of data over time. In this paper, we propose a method based on sliding-window model for which summarizes a graph stream based on a combination of the structure and vertex attributes. We proposed a new structure for summary graphs and also proposed new methods for comparing two summary graphs. To the best of our knowledge, this is the first method that summarizes a graph stream based on both the structure and vertex attributes with varying contributions. Through extensive experiments on real dataset of Amazon co-purchasing products, we have demonstrated the performance of the proposed method.
Highlights
Introduction in supermarketsFor this example, the relationship between sold products are received as a stream of edges, an edge represents each pair of sold products
We propose a method based on sliding-window model for which summarizes a graph stream based on a combination of the structure and vertex attributes
A number of algorithms have been proposed for summarizGraph summarization is a useful and interesting topic that ing stationery attributed graphs based on both the struchas been recently studied in the literature [1] widely
Summary
Community detection algorithms has many applications and recently, many articles [22,23,24,25,26] have been published on this subject. In [33] Feigenbaum et al have been interested in is summarized based on vertex attributes, without take the trade-offs between model parameters such as perinto consideration the graph structure, and by mov- data-item processing time, required space, and the reing nodes between super-nodes adjust the summary to quired number of passes over the stream. In [34] a new variation of streaming model with a graphs which constructs a hybrid summary by considering helper which can provide annotations for data streams MDL principle to model the graph summarization problem have been proposed by Cormode et al They have discussed into a code cost function and utilizing greedy method to that by giving linear sized annotations, the memory for compute an optimal summary In this method, the user’s many problems is reduced to constant time. Stream which converts a graph to a smaller one by removing unnecessary details and preserving overall properties
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