# A Hierarchical Parallel Graph Summarization Approach Based on Ranking Nodes
## 3 Results and Discussion  
### Experimental Setup  
The HRNS was implemented based on an open-source version of greedy summarization ([[https://github.com/mgiridhar/graph_summarization_for_query_evaluation](https://github.com/mgiridhar/graph_summarization_for_query_evaluation)]([https://github.com/mgiridhar/graph_summarization_for_query_evaluation](https://github.com/mgiridhar/graph_summarization_for_query_evaluation)) (accessed on 2 November 2021)). The experiments were performed on a machine with 40 xIntel Intel(R) Xeon(R) CPU E5-2450L (1.7 GHz, 10 cores), 132 GB RAM, and 3.7 TB hard disks, running CentOS release 7.5.1804 (64 bit). The HRNS sets 8 parallel threads by default. To compare these in different conditions, we also evaluated the sequential version of HRNS (noted as SRNS). Moreover, we implemented the greedy and random summarization algorithms [9], and followed the classic metis graph partition algorithm [39] to minimize the overhead and error loss across partitions. The metis version used was gpMetis 5.1.0. The node's importance ranking is composed of four widely used graph metrics, which are Pagerank, Clustering Coefficient, Degree Centrality, and Eigenvector Centrality, respectively. Table 1 lists the open-source graph datasets. The evaluation chooses both real and synthetic datasets, including different domains such as social networks, citation networks, and text links. The 2000-2 and 2500-2 include synthesized data that were obtained via the SNAP ([[https://snap.stanford.edu/snappy/index.html](https://snap.stanford.edu/snappy/index.html)]([https://snap.stanford.edu/snappy/index.html](https://snap.stanford.edu/snappy/index.html)) (accessed on 15 October 2022)) toolkit for UCforum ([[https://toreposahl.com/datasets/#online_forum_network](https://toreposahl.com/datasets/#online_forum_network)]([https://toreposahl.com/datasets/#online_forum_network](https://toreposahl.com/datasets/#online_forum_network)) (accessed on 10 October 2022)) and Facebook ([[https://snap.stanford.edu/data/ego-Facebook.html](https://snap.stanford.edu/data/ego-Facebook.html)]([https://snap.stanford.edu/data/ego-Facebook.html](https://snap.stanford.edu/data/ego-Facebook.html)) (accessed on 18 September 2022)), which are both social networks, for Cora ([[https://linds.org/datasets/#cora](https://linds.org/datasets/#cora)]([https://linds.org/datasets/#cora](https://linds.org/datasets/#cora)) (accessed on 18 September 2022)), Ca-GrQc and Daily Kos ([[http://archive.ics.uci.edu/ml/datasets/Bag+of+Words](http://archive.ics.uci.edu/ml/datasets/Bag+of+Words)]([http://archive.ics.uci.edu/ml/datasets/Bag+of+Words](http://archive.ics.uci.edu/ml/datasets/Bag+of+Words)) (accessed on 17 March 2023)), which belong to the publication network, and for Bible ([[http://moreno.ss.uci.edu/data.html#names](http://moreno.ss.uci.edu/data.html#names)]([http://moreno.ss.uci.edu/data.html#names](http://moreno.ss.uci.edu/data.html#names)) (accessed on 6 October 2022)) and Blogs ([[http://moreno.ss.uci.edu/data.html#blogs](http://moreno.ss.uci.edu/data.html#blogs)]([http://moreno.ss.uci.edu/data.html#blogs](http://moreno.ss.uci.edu/data.html#blogs)) (accessed on 10 October 2022)), which are text networks. The sources of Wikipedia elections ([[http://snap.stanford.edu/data/wiki-Vote.html](http://snap.stanford.edu/data/wiki-Vote.html)]([http://snap.stanford.edu/data/wiki-Vote.html](http://snap.stanford.edu/data/wiki-Vote.html)) (accessed on 15 March 2023)), Wikipedia edits (jbo) ([[http://dumps.wikimedia.org/](http://dumps.wikimedia.org/)]([http://dumps.wikimedia.org/](http://dumps.wikimedia.org/)) (accessed on 17 March 2023)), Wikipedia edits (glk), and Wikipedia edits (nos) were all derived from Wikipedia. Wikipedia elections refers to a network of administrator elections. Wikipedia edits (jbo) represents an author network of the Lojban encyclopedia that is linked together by edit events. Additionally, Wikipedia edits (glk) and Wikipedia edits (nso) are hyperlink networks that showcase articles in the Gilaki and Northern Sotho languages, respectively.