Scalable Substructure Discovery Algorithm For Homogeneous Multilayer Networks

TL;DR

This work tackles scalable substructure discovery in homogeneous multilayer networks (HoMLNs) by introducing a decoupling-based iterative composition approach (Ho-ICA). Each layer is processed independently to enumerate substructures, which are then composed across layers to form inter-layer patterns, with duplicates removed via canonical representations and substructures ranked by Minimum Description Length (MDL) using $MDL = \frac{DL(G)}{DL(S) + DL(G|S)}$. The method is implemented in Map/Reduce, with theoretical proofs of completeness and soundness and extensive experiments on synthetic and real-world graphs showing full accuracy across varying layer distributions and substantial, though non-linear, speedups as resources increase. The results demonstrate scalable, accurate substructure discovery for HoMLNs and highlight practical implications for analyzing complex, multi-typed networks in distributed environments.

Abstract

Graph mining analyzes real-world graphs to find core substructures (connected subgraphs) in applications modeled as graphs. Substructure discovery is a process that involves identifying meaningful patterns, structures, or components within a large data set. These substructures can be of various types, such as frequent patterns, motifs, or other relevant features within the data. To model complex data sets -- with multiple types of entities and relationships -- multilayer networks (or MLNs) have been shown to be more effective as compared to simple and attributed graphs. Analysis algorithms on MLNs using the decoupling approach have been shown to be both efficient and accurate. Hence, this paper focuses on substructure discovery in homogeneous multilayer networks (one type of MLN) using a novel decoupling-based approach. In this approach, each layer is processed independently, and then the results from two or more layers are composed to identify substructures in the entire MLN. The algorithm is designed and implemented, including the composition part, using one of the distributed processing frameworks (the Map/Reduce paradigm) to provide scalability. After establishing the correctness, we analyze the speedup and response time of the proposed algorithm and approach through extensive experimental analysis on large synthetic and real-world data sets with diverse graph characteristics.

Figures (14)

• Figure 1: MLN Types
• Figure 2: Lossy (a), Decoupling (b), and MLN (c) approaches
• Figure 3: Input Graph
• Figure 4: Partitioned Input Graph
• Figure 5: Duplicate Generation

Theorems & Definitions (6)

• Definition 1
• Lemma 6.1
• Lemma 6.2
• Lemma 6.3
• Theorem 6.4
• Lemma 6.5