Dense subgraphs induced by edge labels

• Published in: Machine learning Vol. 113; no. 4; pp. 1967 - 1987
• Main Authors: Kumpulainen, Iiro, Tatti, Nikolaj
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2024; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Computer Science; Control; Graph theory; Graphs; Labels; Machine Learning; Mechatronics; Natural Language Processing (NLP); Networks; Nodes; Robotics; Simulation and Modeling; Social networks; Special Issue on Discovery Science 2022; Subject specialists; Dense subgraphs; Label-induced subgraphs; Convex hull
• ISSN: 0885-6125; 1573-0565
• DOI: 10.1007/s10994-023-06377-y

Finding densely connected groups of nodes in networks is a widely-used tool for analysis in graph mining. A popular choice for finding such groups is to find subgraphs with a high average degree. While useful, interpreting such subgraphs may be difficult. On the other hand, many real-world networks have additional information, and we are specifically interested in networks with labels on edges. In this paper, we study finding sets of labels that induce dense subgraphs. We consider two notions of density: average degree and the number of edges minus the number of nodes weighted by a parameter α . There are many ways to induce a subgraph from a set of labels, and we study two cases: First, we study conjunctive-induced dense subgraphs, where the subgraph edges need to have all labels. Secondly, we study disjunctive-induced dense subgraphs, where the subgraph edges need to have at least one label. We show that both problems are NP -hard. Because of the hardness, we resort to greedy heuristics. We show that we can implement the greedy search efficiently: the respective running times for finding conjunctive-induced and disjunctive-induced dense subgraphs are in O p log k and O p log 2 k , where p is the number of edge-label pairs and k is the number of labels. Our experimental evaluation demonstrates that we can find the ground truth in synthetic graphs and that we can find interpretable subgraphs from real-world networks.