Single- and Multi-level Network Sparsification by Algebraic Distance

@article{John2017SingleAM,
  title={Single- and Multi-level Network Sparsification by Algebraic Distance},
  author={Emmanuel John and Ilya Safro},
  journal={ArXiv},
  year={2017},
  volume={abs/1601.05527}
}
Network sparsification methods play an important role in modern network analysis when fast estimation of computationally expensive properties (such as the diameter, centrality indices, and paths) is required. We propose a method of network sparsification that preserves a wide range of structural properties. Depending on the analysis goals, the method allows to distinguish between local and global range edges that can be filtered out during the sparsification. First we rank edges by their… 
Multilevel Methods for Sparsification and Linear Arrangement Problems on Networks
TLDR
This thesis develops a robust network sparsification method that enables filtering of either, so called, longand short-range edges or both and introduces asymmetric coarsening schemes for multilevel algorithms developed for linear arrangement problems.
Structure-preserving sparsification methods for social networks
TLDR
The first systematic conceptual and experimental comparison of edge sparsification methods on a diverse set of network properties is contributed and it is shown that they can be understood as methods for rating edges by importance and then filtering globally or locally by these scores.
A Framework for Analyzing Resparsification Algorithms
TLDR
This work presents a framework for analyzing algorithms that perform repeated sparsifications that only incur error corresponding to a single sparsification step, leading to better results for many of these reseparsification based algorithms.
Multiscale planar graph generation
TLDR
A flexible algorithm that can synthesize realistic networks that are planar, which preserves the structural properties with minimal bias including the planarity of the network, while introducing realistic variability at multiple scales is presented.
Relaxation-Based Coarsening for Multilevel Hypergraph Partitioning
TLDR
The concept of algebraic distance on hypergraphs is introduced and its use as an algorithmic component in the coarsening stage of multilevel hypergraph partitioning solvers is demonstrated.
Hypergraph Partitioning With Embeddings
TLDR
This work proposes using graph embeddings of the initial hypergraph in order to ensure that coarsened problem instances retrain key structural features, and leads to significantly improved solution quality across a range of considered hypergraphs.
backbone: An R package to extract network backbones
TLDR
A substantially expanded version of the backbone package for R is introduced, which now provides methods for extracting backbones from weighted networks, weighted bipartite projections, and unweighted networks.
Graph Sparsification with Generative Adversarial Network
  • Hang Wu, Yi-Ling Chen
  • Computer Science
    2020 IEEE International Conference on Data Mining (ICDM)
  • 2020
TLDR
This study proposes a novel method called GSGAN, which is able to sparsify networks for community detection tasks and adopts GAN as the learning model and guides the generator to produce random walks that are able to capture the structure of a network.
Aggregative Coarsening for Multilevel Hypergraph Partitioning
TLDR
This paper introduces two novel aggregative coarsening schemes and incorporates them within state-of-the-art hypergraph partitioner Zoltan, inspired by the algebraic multigrid and stable matching approaches.
First- and High-Order Bipartite Embeddings
TLDR
Two embeddings for bipartite graphs that decompose edges into sets of indirect relationships between node neighborhoods that are found to perform better on recommendation tasks and equally competitive in link prediction are proposed.
...
...

References

SHOWING 1-10 OF 67 REFERENCES
Structure-preserving sparsification of social networks
TLDR
The first systematic conceptual and experimental comparison of edge sparsification methods on a diverse set of network properties is contributed and it is shown that they can be understood as methods for rating edges by importance and then filtering globally by these scores.
Local graph sparsification for scalable clustering
TLDR
This paper proposes to rank edges using a simple similarity-based heuristic that is efficiently compute by comparing the minhash signatures of the nodes incident to the edge, to preferentially retain the edges that are likely to be part of the same cluster.
Ranking and Sparsifying a Connection Graph
Abstract Many problems arising in dealing with high-dimensional data sets involve connection graphs in which each edge is associated with both an edge weight and a d-dimensional linear
Coarse-grained topology estimation via graph sampling
TLDR
This paper shows how to efficiently estimate the category graph from a probability sample of nodes, and applies this methodology to a sample of Facebook users to obtain a number of category graphs, such as the college friendship graph and the country friendship graph.
Spectral Sparsification of Graphs
TLDR
It is proved that every graph has a spectral sparsifier of nearly linear size, and an algorithm is presented that produces spectralSparsifiers in time $O(m\log^{c}m)$, where $m$ is the number of edges in the original graph and $c$ is some absolute constant.
Network Sampling: From Static to Streaming Graphs
TLDR
A family of sampling methods based on the concept of graph induction that generalize across the full spectrum of computational models (from static to streaming) while efficiently preserving many of the topological properties of the input graphs.
Relaxation-based coarsening and multiscale graph organization
TLDR
This paper generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the "closeness" between two nodes that is linear in the number of edges in the graph.
Advanced Coarsening Schemes for Graph Partitioning
TLDR
This work compares different matching- and AMG-based coarsening schemes, experiment with the algebraic distance between nodes, and demonstrates computational results on several classes of graphs that emphasize the running time and quality advantages of different coARSening schemes.
Algebraic Distance on Graphs
TLDR
This paper considers an iterative process that smooths an associated value for nearby vertices, and presents a measure of the local connection strength, called the algebraic distance, which is attractive in that the process is simple, linear, and easily parallelized.
Exploring Network Structure, Dynamics, and Function using NetworkX
TLDR
Some of the recent work studying synchronization of coupled oscillators is discussed to demonstrate how NetworkX enables research in the field of computational networks.
...
...