Single-cell RNA-seq quantifies biological heterogeneity across both discrete cell types and continuous cell transitions. Partition-based graph abstraction (PAGA) provides an interpretable graph-like map of the arising data manifold, based on estimating connectivity of manifold partitions (
 https://github.com/theislab/paga
 ). PAGA maps preserve the global topology of data, allow analyzing data at different resolutions, and result in much higher computational efficiency of the typical exploratory data analysis workflow. We demonstrate the method by inferring structure-rich cell maps with consistent topology across four hematopoietic datasets, adult planaria and the zebrafish embryo and benchmark computational performance on one million neurons.

/pdf/paga-graph-abstraction-reconciles-clustering-with-trajectory-24es3xt2r5.pdf

PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells

Cluster Layout Planarity testing Booth/Lueker and Boyer/Myrvold Cluster (Feng et al) Upward (Bertolazzi et al) Customizable planarization method Edge insertion (fixed & variable embedding) Crossing Minimization optimal, minor-monotone, simultaneous Orthogonal layout Compaction (constructive + improvement) Customizable Sugiyama layout Energy-based layout (FM, ) Tree-, Circular-, Balloon-layout, 

The Open Graph Drawing Framework (OGDF)

The graph partitioning problem is widely used and studied in many practical and theoretical applications. Today, multilevel strategies represent one of the most effective and efficient generic frameworks for solving this problem on large-scale graphs. Most of the attention in designing multilevel partitioning frameworks has been on the refinement phase. In this work, we focus on the coarsening phase, which is responsible for creating structures similar to the original but smaller graphs. We compare different matching- and AMG-based coarsening schemes, experiment with the algebraic distance between nodes, and demonstrate computational results on several classes of graphs that emphasize the running time and quality advantages of different coarsening schemes.

/pdf/advanced-coarsening-schemes-for-graph-partitioning-342dvkwz1z.pdf

Advanced Coarsening Schemes for Graph Partitioning

With the prevalence of big data, there is a growing need for algorithms and techniques for visualizing very large and complex graphs. In this article, we review layout algorithms and interactive exploration techniques for large graphs. In addition, we briefly look at softwares and datasets for visualization graphs, as well as challenges that need to be addressed. WIREs Comput Stat 2015, 7:115-136. doi: 10.1002/wics.1343

/pdf/visualizing-large-graphs-1m49gjmigt.pdf

Visualizing large graphs

The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on large-scale graphs. Most of the attention in designing the multilevel partitioning frameworks has been on the refinement phase. In this work we focus on the coarsening phase, which is responsible for creating structurally similar to the original but smaller graphs. We compare different matching- and AMG-based coarsening schemes, experiment with the algebraic distance between nodes, and demonstrate computational results on several classes of graphs that emphasize the running time and quality advantages of different coarsenings.

Applying the multilevel paradigm to energy-based layout algorithms can improve both the quality of the resulting drawings as well as the running time of the layout computation. In order to do this, approaches for the different multilevel phases refinement, placement, layout, and optionally scaling and postprocessing need to be implemented. A number of multilevel layout algorithms have been proposed already, which differ in the way these phases are realized. We present an experimental study that investigates the influence of varying combinations with respect to running time and quality criteria.

/pdf/an-experimental-evaluation-of-multilevel-layout-methods-qk7eg7ccjp.pdf

An experimental evaluation of multilevel layout methods

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An experimental evaluation of multilevel layout methods