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frb45-21-4     (BHOSLIB)

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This network dataset is in the category of BHOSLIB



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Metadata

CategoryDense Networks
CollectionBHOSLIB
Tags
FormatUndirected
Edge weightsUnweighted
DescriptionBenchmark graphs for testing several NP-hard graph algorithms including but not limited to the maximum clique problem, maximum independent set, minimum vertex cover and vertex coloring.

Please cite the following if you use the data:

@inproceedings{nr,
     title={The Network Data Repository with Interactive Graph Analytics and Visualization},
     author={Ryan A. Rossi and Nesreen K. Ahmed},
     booktitle={AAAI},
     url={https://networkrepository.com},
     year={2015}
}

Note that if you transform/preprocess the data, please consider sharing the data by uploading it along with the details on the transformation and reference to any published materials using it.

@misc{BHOSLIB,
     author={BHOSLIB},
     title={Benchmarks with hidden optimum solutions for graph problems},
     year={2004}
}

@inproceedings{cai2012two,
     title={Two new local search strategies for minimum vertex cover},
     author={Cai, Shaowei and Su, Kaile and Sattar, Abdul},
     booktitle={Twenty-Sixth AAAI Conference on Artificial Intelligence},
     year={2012}
}

@article{rossi2014coloring,
     title={Coloring Large Complex Networks},
     author={Ryan A. Rossi and Nesreen K. Ahmed},
     booktitle={Social Network Analysis and Mining},
     pages={1--51},
     year={2014}
}

Network Data Statistics

Nodes945
Edges387.5K
Density0.868736
Maximum degree875
Minimum degree732
Average degree820
Assortativity-0.028105
Number of triangles275.7M
Average number of triangles291.8K
Maximum number of triangles331.2K
Average clustering coefficient0.868019
Fraction of closed triangles0.867953
Maximum k-core757
Lower bound of Maximum Clique36

Network Data Preview

Interactive visualization of frb45-21-4's graph structure

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Interactive Visualization of Node-level Properties and Statistics

Tools for Interactive Exploration of Node-level Statistics

Visualize and interactively explore frb45-21-4 and its important node-level statistics!

  • Each point represents a node (vertex) in the graph.
  • A subset of interesting nodes may be selected and their properties may be visualized across all node-level statistics. To select a subset of nodes, hold down the left mouse button while dragging the mouse in any direction until the nodes of interest are highlighted.This feature allows users to explore and analyze various subsets of nodes and their important interesting statistics and properties to gain insights into the graph data
  • Zoom in/out on the visualization you created at any point by using the buttons below on the left.
  • Once a subset of interesting nodes are selected, the user may further analyze by selecting and drilling down on any of the interesting properties using the left menu below.
  • We also have tools for interactively visualizing, comparing, and exploring the graph-level properties and statistics.
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Interactive Visualization of Node-level Feature Distributions

Node-level Feature Distributions

degree distribution

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degree CDF

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degree CCDF

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kcore distribution

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kcore CDF

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kcore CCDF

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triangle distribution

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triangle CDF

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triangle CCDF

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All visualizations and analytics are interactive and flexible for exploratory analysis and data mining in real-time and include the following features:

  • Degree, k-core, triangles, and triangle-core distributions. We include plots for each of the fundamental graph features and counts of the number with a particular property (i.e., number of nodes that form k triangles or have degree k, etc.)
  • We also include the CDF and CCDF distributions for each graph in the collection.
  • All visualizations and plots are zoomable. One may zoom-in or out on the data visualization using scrolling.
  • Panning. Users may also click anywhere on the plot and move the mouse in any direction to pan.
  • Adjust scale and other application dependent-parameters. All interactive visualizations may adjust the scale which is particularly important in certain types of graph data that contain highly skewed graph properties (power-lawed graphs and/or networks) such as degree distribution.