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k-peak decomposition
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This is the python code for performing k-peak decomposition and plotting mountain plots.

If using k-peak decomposition or the mountain-plot, please cite the following paper:

Priya Govindan, Chenghong Wang, Chumeng Xu, Hongyu Duan, Sucheta Soundarajan. The k-peak decomposition: Mapping the global structure of graphs.  WWW 2017

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Graph Input: 
- Format: Undirected, unweighted graph in the form of a text file of comma separated edge-list. An example input file, ‘toygraph.txt’, is provided. 
- Reading the graph: The graph is to be read a Networkx graph. The file ‘sample_usage.py’ demonstrates how to read the input file and call the functions to compute k-peak decomposition and create mountain-plots.
- Note that we assume that every node has at least one edge. Singletons are removed before k-peak decomposition is done. Singletons have core and peak number of 0.
- Self-loops are ignored.


Required packages:
Networkx - https://networkx.github.io/
Matplotlib - http://matplotlib.org/


Key functions in ‘kpeak_decomposition.py’:

1. get_kpeak_decomposition : Given a graph, it computes the peak number of every node in the graph. Input is a a Networkx graph object. Output is a dictionary of core numbers and a dictionary of peak numbers. The keys in both dictionaries are node IDs and the values are the peak or core number.

2. draw_mountainplot : Given a graph, it creates the mountain-plot of the graph. Input is a a networkx graph object and a graph name in String. Output is a PDF file of the mountain-plot in the same directory as the code.

3. draw_mountainplot_components : Given a graph, it creates the mountain-plot of the graph. Input is a a networkx graph object and a graph name in String. Output is a PDF file of the mountain-plot in the same directory as the code.  draw_mountainplot_components differs from draw_mountainplot in that mountains with multiple components are depicted separately.

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CITATION:
Priya Govindan, Chenghong Wang, Chumeng Xu, Hongyu Duan, and Sucheta Soundarajan. 2017. The k-peak Decomposition: Mapping the Global Structure of Graphs. In Proceedings of the 26th International Conference on World Wide Web (WWW '17). International World Wide Web Conferences Steering Committee, Republic and Canton of Geneva, Switzerland, 1441-1450. DOI: https://doi.org/10.1145/3038912.3052635


BIBTEX:
BibTeX | EndNote | ACM Ref
@inproceedings{Govindan:2017:KDM:3038912.3052635,
 author = {Govindan, Priya and Wang, Chenghong and Xu, Chumeng and Duan, Hongyu and Soundarajan, Sucheta},
 title = {The K-peak Decomposition: Mapping the Global Structure of Graphs},
 booktitle = {Proceedings of the 26th International Conference on World Wide Web},
 series = {WWW '17},
 year = {2017},
 isbn = {978-1-4503-4913-0},
 location = {Perth, Australia},
 pages = {1441--1450},
 numpages = {10},
 url = {https://doi.org/10.1145/3038912.3052635},
 doi = {10.1145/3038912.3052635},
 acmid = {3052635},
 publisher = {International World Wide Web Conferences Steering Committee},
 address = {Republic and Canton of Geneva, Switzerland},
 keywords = {graph visualization, graphs, k-core, k-peak},
}