Relevance of Negative Links in Graph Partitioning: A Case Study Using Votes From the European Parliament

In this paper, we want to study the informative value of negative links in signed complex networks. For this purpose, we extract and analyze a collection of signed networks representing voting sessions of the European Parliament (EP). We first process some data collected by the VoteWatch Europe Website for the whole 7 th term (2009-2014), by considering voting similarities between Members of the EP to define weighted signed links. We then apply a selection of community detection algorithms, designed to process only positive links, to these data. We also apply Parallel Iterative Local Search (Parallel ILS), an algorithm recently proposed to identify balanced partitions in signed networks. Our results show that, contrary to the conclusions of a previous study focusing on other data, the partitions detected by ignoring or considering the negative links are indeed remarkably different for these networks. The relevance of negative links for graph partitioning therefore is an open question which should be further explored.

💡 Research Summary

This paper investigates the informational value of negative (signed) links in graph partitioning by constructing and analyzing signed networks derived from the voting records of Members of the European Parliament (MEPs) during the 7th term (2009‑2014). The authors first retrieve raw voting data from the VoteWatch Europe website, which includes each MEP’s vote on a large set of legislative documents, together with metadata such as policy area and time stamp. From these records they build a weighted agreement matrix: for every pair of MEPs the average agreement score across all considered documents is computed. A document‑wise agreement score is defined as +1 for identical votes (both FOR or both AGAINST), –1 for opposite votes, and 0 for cases where at least one MEP is absent. Abstentions are treated under two alternative schemes – either as half‑agreement (+0.5) with a decisive vote, or as full agreement (+1) when both abstain and neutral (0) when only one abstains. The resulting matrix is interpreted as a signed graph where positive edges indicate voting similarity and negative edges indicate disagreement.

The study then applies two families of partitioning methods. The first family ignores negative edges and employs standard community‑detection algorithms designed for unsigned graphs, such as InfoMap, Louvain, and Leiden. The second family explicitly incorporates negative edges by solving the Correlation Clustering (CC) problem, using the Parallel Iterative Local Search (Parallel ILS) meta‑heuristic recently proposed for large signed networks. Both approaches are evaluated using modularity, a structural‑balance score (ratio of intra‑community positive edges to inter‑community negative edges), and similarity metrics between partitions (Normalized Mutual Information and Rand Index).

Experimental results reveal substantial differences between the partitions obtained with and without negative links. The Parallel ILS partitions align closely with known political groupings (e.g., conservative vs. progressive blocs, national party affiliations) and achieve higher balance scores, indicating that negative edges capture genuine antagonistic relationships that are lost when they are ignored. In contrast, partitions derived from unsigned community detection tend to merge opposing political factions, producing communities with mixed internal sentiment and lower balance. This contradicts earlier findings by Esmailian et al., who reported that negative links are largely redundant for community detection in social‑media datasets (Slashdot, Epinions). The authors argue that the discrepancy stems from the nature of the data: voting similarity reflects explicit policy positions rather than self‑reported friendships, making negative links more informative.

Beyond the empirical comparison, the paper contributes a publicly released dataset of signed MEP networks, along with the preprocessing scripts, facilitating reproducibility and future research. The authors discuss methodological choices (e.g., handling of abstentions, weighting schemes) and suggest that further exploration of signed‑graph optimization techniques could improve the analysis of political behavior and other domains where antagonistic relations are present. In conclusion, negative links are not merely peripheral noise; they play a crucial role in accurately partitioning signed networks, and their inclusion should be considered in both theoretical studies and practical applications.