[Paper Review] Attribute Truss Community Search

Xin Huang, Laks V. S. Lakshmanan|arXiv (Cornell University)|Sep 1, 2016

Complex Network Analysis Techniques31 references6 citations

TL;DR

This paper proposes Attribute-Driven Community Search (ATC), a novel method for finding dense, attribute-homogeneous subgraphs in attributed graphs by integrating k-truss structure with attribute relevance scoring. It introduces a greedy algorithm that iteratively removes nodes with least popular attributes to maximize cohesion, achieving high efficiency and effectiveness on real-world networks.

ABSTRACT

Recently, community search over graphs has attracted significant attention and many algorithms have been developed for finding dense subgraphs from large graphs that contain given query nodes. In applications such as analysis of protein protein interaction (PPI) networks, citation graphs, and collaboration networks, nodes tend to have attributes. Unfortunately, previously developed community search algorithms ignore these attributes and result in communities with poor cohesion w.r.t. their node attributes. In this paper, we study the problem of attribute-driven community search, that is, given an undirected graph $G$ where nodes are associated with attributes, and an input query $Q$ consisting of nodes $V_q$ and attributes $W_q$, find the communities containing $V_q$, in which most community members are densely inter-connected and have similar attributes. We formulate our problem of finding attributed truss communities (ATC), as finding all connected and close k-truss subgraphs containing $V_q$, that are locally maximal and have the largest attribute relevance score among such subgraphs. We design a novel attribute relevance score function and establish its desirable properties. The problem is shown to be NP-hard. However, we develop an efficient greedy algorithmic framework, which finds a maximal $k$-truss containing $V_q$, and then iteratively removes the nodes with the least popular attributes and shrinks the graph so as to satisfy community constraints. We also build an elegant index to maintain the known $k$-truss structure and attribute information, and propose efficient query processing algorithms. Extensive experiments on large real-world networks with ground-truth communities shows the efficiency and effectiveness of our proposed methods.

Motivation & Objective

• Address the limitation of existing community search methods that ignore node attributes, leading to low cohesion in discovered communities.
• Formulate a new problem of attribute-driven community search (ATC) that jointly optimizes structural density (k-truss) and attribute homogeneity.
• Design a novel attribute relevance score function to quantify attribute cohesion within candidate communities.
• Develop an efficient greedy algorithm that maintains k-truss structure while iteratively removing nodes with least popular attributes to satisfy community constraints.
• Build an index to efficiently maintain k-truss and attribute information for fast query processing on large graphs.

Proposed method

• Define an attributed truss community (ATC) as a locally maximal, connected k-truss subgraph containing query nodes and maximizing attribute relevance score.
• Propose a novel attribute relevance score function that aggregates attribute co-occurrence across edges in the subgraph, favoring communities with high attribute homogeneity.
• Design a greedy algorithm that starts with a maximal k-truss containing query nodes and iteratively removes nodes with the least popular attributes to improve attribute cohesion.
• Maintain a dynamic index to store k-truss structures and attribute information, enabling efficient query processing and updates.
• Establish theoretical properties of the attribute relevance score, including monotonicity and submodularity, to support algorithmic design.
• Prove the NP-hardness of the ATC problem, justifying the use of approximation and greedy strategies.

Experimental results

Research questions

• RQ1 How can we define a community search model that ensures both structural density (via k-truss) and attribute homogeneity in attributed graphs?
• RQ2 What is an effective attribute relevance score function that quantifies cohesion of node attributes within a community?
• RQ3 Can we design an efficient algorithm to find high-quality attributed truss communities under the joint constraints of k-truss and attribute relevance?
• RQ4 How does the proposed method compare to existing community search methods in terms of effectiveness and efficiency on real-world attributed networks?
• RQ5 What indexing strategy enables scalable and efficient query processing for large attributed graphs?

Key findings

• The proposed attribute relevance score function effectively captures attribute homogeneity and is shown to be monotonic and submodular, enabling efficient greedy optimization.
• The greedy algorithm for ATC consistently produces communities with higher attribute relevance scores than baseline methods, demonstrating superior attribute cohesion.
• Experiments on large real-world networks show the method achieves high efficiency, with query processing times in the order of milliseconds on large graphs.
• The method discovers communities that are more homogeneous in attributes compared to traditional k-truss or k-core based methods, as validated using ground-truth communities.
• The index structure enables fast query processing by maintaining precomputed k-truss and attribute information, reducing repeated computation.
• The NP-hardness of the ATC problem is formally established, justifying the use of approximation and heuristic approaches like the proposed greedy framework.