Q-DISCO: Query-Centric Densest Subgraphs in Networks with Opinion Information

TL;DR

This paper introduces heuristic algorithms to identify dense subgraphs with aligned opinions in social networks, addressing an NP-hard problem with practical applications demonstrated on Twitter datasets related to current events.

Contribution

The paper formulates the query-centric densest subgraph problem with opinion data, proves its NP-hardness, and proposes two heuristic algorithms with theoretical analysis and empirical validation.

Findings

Algorithms effectively extract meaningful opinion-aligned communities.

Heuristics perform well on real-world Twitter datasets.

Method provides insights into opinion formation and dissemination.

Abstract

Given a network $G=(V,E)$, where each node $v$ is associated with a vector $\boldsymbol{p}_v \in \mathbb{R}^d$ representing its opinion about $d$ different topics, how can we uncover subsets of nodes that not only exhibit exceptionally high density but also possess positively aligned opinions on multiple topics? In this paper we focus on this novel algorithmic question, that is essential in an era where digital social networks are hotbeds of opinion formation and dissemination. We introduce a novel methodology anchored in the well-established densest subgraph problem. We analyze the computational complexity of our formulation, indicating that our problem is NP-hard and eludes practically acceptable approximation guarantees. To navigate these challenges, we design two heuristic algorithms: the first is predicated on the Lagrangian relaxation of our formulation, while the second adopts a peeling algorithm based on the dual of a Linear Programming relaxation. We elucidate the theoretical underpinnings of their performance and validate their utility through empirical evaluation on real-world datasets. Among others, we delve into Twitter datasets we collected concerning timely issues, such as the Ukraine conflict and the discourse surrounding COVID-19 mRNA vaccines, to gauge the effectiveness of our methodology. Our empirical investigations verify that our algorithms are able to extract valuable insights from networks with opinion information.