BC tree-based spectral sampling for big complex network visualization

Graph sampling methods have been used to reduce the size and complexity of big complex networks for graph mining and visualization. However, existing graph sampling methods often fail to preserve the connectivity and important structures of the original graph. This paper introduces a new divide and conquer approach to spectral graph sampling based on graph connectivity, called the BC Tree (i.e., decomposition of a connected graph into biconnected components) and spectral sparsification. Specifically, we present two methods, spectral vertex sampling $$BC\_SV$$ B C _ S V and spectral edge sampling $$BC\_SS$$ B C _ S S by computing effective resistance values of vertices and edges for each connected component. Furthermore, we present $$DBC\_SS$$ D B C _ S S and $$DBC\_GD$$ D B C _ G D , graph connectivity-based distributed algorithms for spectral sparsification and graph drawing respectively, aiming to further improve the runtime efficiency of spectral sparsification and graph drawing by integrating connectivity-based graph decomposition and distributed computing. Experimental results demonstrate that $$BC\_SV$$ B C _ S V and $$BC\_SS$$ B C _ S S are significantly faster than previous spectral graph sampling methods while preserving the same sampling quality. $$DBC\_SS$$ D B C _ S S and $$DBC\_GD$$ D B C _ G D obtain further significant runtime improvement over sequential approaches, and $$DBC\_GD$$ D B C _ G D further achieves significant improvements in quality metrics over sequential graph drawing layouts.

CoSEP: A compound spring embedder layout algorithm with support for ports

This paper describes a new automatic layout algorithm named CoSEP for compound graphs with port constraints. The algorithm works by extending the physical model of a previous algorithm named CoSE by defining additional force types and heuristics for constraining edges to connect to certain user-defined locations on end nodes. Similar to its predecessor, CoSEP also accounts for non-uniform node dimensions and arbitrary levels of nesting via compound nodes. Our experiments show that CoSEP significantly improves the quality of the layouts for compound graphs with port constraints with respect to commonly accepted graph drawing criteria while running reasonably fast, suitable for use in interactive applications for small to medium-sized (up to 500 nodes) graphs. A complete JavaScript implementation of CoSEP as a Cytoscape.js extension along with a demo page is freely available at https://github.com/iVis-at-Bilkent/cytoscape.js-cosep .

Graph Drawing Approaches for Petri Net Visualisation and Representation

Petri net structures can benefit from being modelled using graph drawing approaches. This work presents some advanced graph drawing approaches that can be used for visualising Petri net models. These are i) topological shape metrics, ii) visibility drawing, iii) orthogonalization, iv) hierarchical and v) bi-graph partitioning. The models show that this can be successfully done and the Petri nets that are generated in this work are suitable for visualisation. Graph visualisation is an important topic and the results show that there is a large potential to apply this approach to drawing Petri Nets in novel ways.

Mental Map-Preserving Visualization through a Genetic Algorithm

The video game industry has evolved significantly, with different genres becoming popular over time, but how to visualize such information by curating data into a form that makes it easier to identify and understand the trends is quite an interesting research topic. This research focuses on producing an animation of aesthetically pleasing two-dimensional (2D) undirected graphs based on PC video game datasets. The data are further analyzed for developing a web-based application giving users the ability to control and create the animation of a graph. To make it easier to understand the animation of a graph, the changes between the displays of the previous and the following periods are set as small as possible, allowing a user to grasp the differences of the graph’s structure faster. A genetic algorithm-based undirected graph drawing that minimizes both the aesthetic criteria and mental map cost are proposed in this research to tackle this problem. Furthermore, based on our experiments, we could find the best period to start with, so we do not necessarily need to start from the first period to calculate the animation result. Our experiment results proved that a smoother animation could be achieved, and information is better preserved throughout the animation.