[Paper Review] The Slashdot Zoo: Mining a Social Network with Negative Edges

Jérôme Kunegis, Andreas Lommatzsch+1 more|arXiv (Cornell University)|Oct 31, 2017

Complex Network Analysis Techniques27 references392 citations

TL;DR

This paper introduces signed network analysis techniques for social networks with positive (friend) and negative (foe) edges, using the Slashdot Zoo dataset. It proposes algebraic methods based on matrix exponentials and signed Laplacians to model multiplicative transitivity—'the enemy of my enemy is my friend'—demonstrating that these methods significantly outperform traditional unsigned approaches in predicting link signs and identifying unpopular users.

ABSTRACT

We analyse the corpus of user relationships of the Slashdot technology news site. The data was collected from the Slashdot Zoo feature where users of the website can tag other users as friends and foes, providing positive and negative endorsements. We adapt social network analysis techniques to the problem of negative edge weights. In particular, we consider signed variants of global network characteristics such as the clustering coefficient, node-level characteristics such as centrality and popularity measures, and link-level characteristics such as distances and similarity measures. We evaluate these measures on the task of identifying unpopular users, as well as on the task of predicting the sign of links and show that the network exhibits multiplicative transitivity which allows algebraic methods based on matrix multiplication to be used. We compare our methods to traditional methods which are only suitable for positively weighted edges.

Motivation & Objective

• To develop and evaluate signed network analysis techniques for social networks with negative edge weights.
• To investigate whether multiplicative transitivity ('enemy of my enemy is my friend') holds in real-world signed networks.
• To identify unpopular users using novel signed centrality and popularity measures.
• To predict the sign of social network links using algebraic similarity measures based on matrix functions.
• To compare the performance of signed algebraic methods against traditional unsigned network analysis techniques.

Proposed method

• Proposes a signed clustering coefficient and relative signed clustering coefficient to analyze global network structure.
• Introduces Negative Rank as a signed popularity measure to identify unpopular or troll users.
• Adapts spectral similarity measures (e.g., matrix exponential, symmetric and asymmetric matrix exponentials, signed Laplacian) for link sign prediction.
• Uses dimensionality reduction via eigendecomposition to compute matrix exponentials and pseudoinverses efficiently.
• Applies the matrix exponential kernel to model long-range multiplicative transitivity with damping.
• Employs a 30% holdout test set to evaluate link sign prediction accuracy using the sign of similarity scores.

Experimental results

Research questions

• RQ1 Does multiplicative transitivity, as in 'enemy of my enemy is my friend', hold in real signed social networks like Slashdot Zoo?
• RQ2 Can signed spectral similarity measures outperform traditional unsigned methods in predicting the sign of social links?
• RQ3 How effective are signed centrality and popularity measures in identifying unpopular or troll users?
• RQ4 Do matrix exponential-based kernels generalize better than non-exponential counterparts in signed network analysis?
• RQ5 Is the asymmetric formulation of matrix kernels more effective than symmetric ones in capturing directional transitivity in signed networks?

Key findings

• The asymmetric matrix exponential kernel achieved the highest prediction accuracy of 0.68, significantly outperforming other methods.
• Exponential kernels showed no overfitting with increasing dimensionality k, achieving asymptotic performance, unlike non-exponential counterparts.
• The signed Laplacian similarity matrix provided stable performance with good accuracy even at low k values and without overfitting.
• The signed clustering coefficient revealed strong evidence of multiplicative transitivity in the Slashdot Zoo network.
• Negative Rank effectively identified unpopular users, demonstrating the utility of signed popularity measures in community detection.
• The study confirms that multiplicative transitivity is a valid and exploitable property in real signed social networks, enabling algebraic methods based on matrix multiplication.