# Big Graph Mining: Algorithms And Discoveries - Inria

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are joined together to form the strong ‘core’ after the gelling point. 5.3 analysis. 3. Graph Compression. An effective way to tackle the problem of growing graphs sizes is to use compression. Compression not only saves disk space, but it also helps running time because disks are much slower than CPU. A challenge in graph compression is to support various graph queries without uncompressing all the data; e.g., in GBASE [25] only small portion of the compressed data is uncompressed to answer graph queries. Another challenge is to design a good graph partition or clustering algorithm for real world graphs, since sparsely connected dense clusters can improve the compression rate. The problem is that real world graphs are often very hard to be partitioned [32]. A promising direction is to exploit the power law characteristic of real world graphs for clustering the edges (e.g. see [20]). 4. Time Evolving Graphs. Many real world graphs are evolving over time; thus efficiently and effectively mining time evolving graphs can lead to interesting discoveries that could not be observed in static graphs. A promising approach is to use tensor (multi-dimensional array) to model time evolving graphs by using the time as the 3rd dimension, and find correlations between dimensions using tensor decompositions (e.g. see [24; 29]). 5. Visualization and Understanding of Graphs. A graph forms a complicated object with many interaction between nodes. Visualization of graphs helps us better understand the structure and the interactions in graphs. The challenge is to effectively summarize the graphs so that users can easily understand the graphs in a screen with limited resolution. Spectral Analysis What are the patterns and anomalies from the spectral analysis of real world graphs? We present interesting discoveries on the tightly connected communities and anomalous nodes. Near-Clique Detection. The spectral analysis of graphs can reveal near cliques, or tightly connected nodes. For this task we analyze the eigenspoke [42] pattern in real world graphs. Eigenspoke is a set of clear lines in the EE-plot which is the scatter plot of the two eigenvectors of the adjacency matrix of the gra

In this paper we describe Pegasus, a big graph mining sys-tem built on top of MapReduce, a modern distributed data processing platform. We introduce GIM-V, an important primitive that Pegasus uses for its algorithms to analyze structures of large graphs. We also introduce HEigen, a large scale eigensolver which is also a part of Pegasus. Both

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