#Jmp separating x s on graph builder how to

In this paper, we introduce a novel perspective regarding the network summarization problem based on concepts from spectral graph theory. Previous works have primarily focused on some type of network partitioning strategies with application-dependent regularizations, most often resulting in strongly connected clusters. Network summarization techniques are commonly used to reduce the computational load while attempting to maintain the basic structural properties of the original network. The occurrence of large-scale networks presents significant computational challenges to process, analyze, and extract information from such networks. Large-scale networks are widely used to represent object relationships in many real world applications.

Using the summary to answer queries is very efficient as the running time to compute the answer depends on the number of supernodes in the summary, rather than the number of nodes in the original graph.

#Jmp separating x s on graph builder how to

We discuss how to use our summaries to store a (lossy or lossless) compressed graph representation and to approximately answer a large class of queries about the original graph, including adjacency, degree, eigenvector centrality, and triangle and subgraph counting. By exposing a connection between graph summarization and geometric clustering problems (i.e., k-means and k-median), we develop the first polynomial-time approximation algorithms to compute the best possible summary of a certain size under both measures. To quantify the dissimilarity between the original graph and a summary, we adopt the reconstruction error and the cut-norm error.

The superedge weights are the edge densities between vertices in the corresponding supernodes. In this work we study a very natural type of summary: the original set of vertices is partitioned into a small number of supernodes connected by superedges to form a complete weighted graph. Given a large graph we aim at producing a concise lossy representation (a summary) that can be stored in main memory and used to approximately answer queries about the original graph much faster than by using the exact representation. We study the problem of graph summarization.