DOI: 10.6084/m9.figshare.8233340.v5
title: Space of optimal solutions of the Correlation Clustering problem on Complete Signed Graphs

description: This is the data used in the experiments of our paper:<br><i>N. Arinik, R. Figueiredo, V. Labatut (2020), Multiplicity and Diversity: Analyzing the Optimal Solution Space of the Correlation Clustering Problem on Complete Signed Graphs, Journal of Complex Networks, DOI: 10.1093/comnet/cnaa025.</i> The code source is accessible here: <i>https://github.com/CompNet/Sosocc</i><br><br>This dataset contains:<br>* Plot files used in the article<br>* Input signed networks<br>* All optimal solutions (i.e. optimal solution space) of the corresponding networks* Evaluation files<br><br><br><br><b># PLOT FILES</b><br>* `<i>Figure1.zip</i>`: Figures showing that there might be many distinct optimal solutions of a small-sized network.<br>* `<i>Figure2.zip</i>`: Figures showing that distinct optimal solutions of a given network might be partition-wise very similar or different.<br>* `<i>Figure4: All Results.zip</i>`: Figure 4 in the article contains only a few plots regarding the results for space considerations. This zip file contains all plots, and it is organized by the values of `<i>l<sub>0</sub></i>`. In each `<i>l<sub>0</sub></i>` folder, the results are shown in three different perspectives:<br> --- Detected Imbalance Percentage vs Graph Order (i.e. number of vertices)<br> --- Prop mispl vs Graph order<br> --- Graph order vs Prop mispl<br>* `<i>workflow.pdf</i>`: The workflow of the methodology used in the article.<br>* `<i>Syrian network With All Solutions.pdf</i>`: Syrian network (on top) with core part information through node colors, and its optimal solutions in which node colors represent partition information (on bottom).<br><br><br><br><b>#NETWORKS</b><br>All networks are in `<i>Input Signed Networks.tar.gz</i>`.<br>Networks are generated through a simple random model (available in <i>https://github.com/CompNet/SignedBenchmark</i>) designed to produce complete (or uncomplete) unweighted networks with built-in modular structure. <br>There are 3 parameters used for the generation:<br>- number of nodes (`<i>n</i>`)<br>- initial number of modules (`<i>l<sub>0</sub></i>`)<br>- proportion of misplaced links, i.e. proportion of frustrated links, (`<i>q<sub>m</sub></i>`)<br><br>Inside `<i>Input Signed Networks.tar.gz</i>`:<br><br>NETWORKS<br>|__n=NB-NODE_l0=INIT_NB_MODULE_dens=1.0000<br>....|__propMispl=PROP_MISPL<br> ........|__propNeg=PROP_NEG<br> ............|__network=NETWORK_NO<br><br>- The first hierarchy =&gt; the folders are named as follows: n=NB-NODE_l0=INIT-NB-MODULE_dens=1.0000<br> The number of nodes, the initial number of modules and the network density are given. The network density is always 1, since we treat only complete signed networks.<br>- The second hierarchy =&gt; the folders are named as follows: propMispl=PROP_MISPL<br> Proportion of misplaced links is given.<br>- The third hierarchy =&gt; the folders are named as follows: propNeg=PROP_NEG<br> Proportion of negative links (`<i>q<sub>n</sub></i>`) is specified. `<i>q<sub>n</sub></i>` changes depending on `<i>n</i>` and `<i>l<sub>0</sub></i>`. Since only complete signed networks are studied, this parameter is automatically computed from the other input parameters.<br>- The fourth hierarchy =&gt; the folders are named as follows: network=NETWORK_NO<br> Network numbers are shown.<br>In the end, thre are three file formats describing the same network content: GraphML (.graphml), Pajek NET (.net) or .G format.<br><br><br><br><b># PARTITIONS</b><br>All partition results are in `<i>Partition Results.tar.gz</i>`. Note that all optimal partitions of a signed network are obtained through an exact partitioning method. The code source is accessible here: <i>https://github.com/arinik9/ExCC</i><br>Inside `<i>Partition Results.tar.gz</i>`:<br><br>PARTITIONS<br>|__n=NB-NODE_l0=INIT_NB_MODULE_dens=1.0000<br> ....|__propMispl=PROP_MISPL<br> ........|__propNeg=PROP_NEG<br> ............|__network=NETWORK_NO<br> ................|__"<i>ExCC-all</i>"<br> ....................|__"<i>signed-unweighted</i>"<br><br>- The first hierarchy =&gt; the folders are named as follows: n=NB-NODE_l0=INIT-NB-MODULE_dens=1.0000<br>- The second hierarchy =&gt; the folders are named as follows: propMispl=PROP_MISPL<br>- The third hierarchy =&gt; the folders are named as follows: propNeg=PROP_NEG<br>- The fourth hierarchy =&gt; the folders are named as follows: network=NETWORK_NO<br>- The fifth hierarchy =&gt; the folders are named as follows: "<i>ExCC-all</i>"<br> The name of the partitioning method are shown. Since an exact partitioning method is used to obtain all distinct optimal solutions, it is named as "<i>ExCC-all</i>".<br>- The sixth hierarchy =&gt; the folders are named as follows: "<i>signed-unweighted</i>"<br> The type of signed networks are shown: signed and unweighted<br>In the end, the partition results are located, and the file names are named as follows: <i>membership.txt</i>. Note that the first partition result number starts from zero.<br><br><b># EVALUATIONS</b><br>Evaluation results related to our plots are in `<i>Evaluation Results.tar.gz</i>. Note that the hierarchy of this folder is the same as that of 'Partitions'. Inside `<i>Evaluation</i><i> Results.tar.gz</i>`:<br>- `Best-k-for-kmedoids.csv`: It contains three columns. 1) the number of solution classes via kmedoids, 2) the best Silhouette score, 3) the best clustering in terms of Silhouette score, which represents solution classes.<br>- `class-core-part-size-tresh=1.00.csv`. It indicates the proportion of core part size for each solution class.<br>- `exec-time.csv`: It indicates the execution time in seconds.<br>- `imbalance.csv`: It contains the information of imbalance as 1) count and 2) percentage <br>- `nb-solution.csv`: It indicates the total number of solutions<br><br><br>