[Paper Review] Network comparison using directed graphlets

David Aparício, Pedro Ribeiro+1 more|arXiv (Cornell University)|Nov 6, 2015

Bioinformatics and Genomic Networks39 references18 citations

TL;DR

This paper proposes directed graphlets as a generalization of undirected graphlets to capture directional topology in biological networks. By extending graphlet analysis to directed networks using a g-trie data structure, the authors introduce gtrieScanner—a highly efficient tool that outperforms state-of-the-art methods in speed and supports arbitrary-sized directed and undirected graphlets, enabling accurate network classification by type.

ABSTRACT

With recent advances in high-throughput cell biology the amount of cellular biological data has grown drastically. Such data is often modeled as graphs (also called networks) and studying them can lead to new insights into molecule-level organization. A possible way to understand their structure is by analysing the smaller components that constitute them, namely network motifs and graphlets. Graphlets are particularly well suited to compare networks and to assess their level of similarity but are almost always used as small undirected graphs of up to five nodes, thus limiting their applicability in directed networks. However, a large set of interesting biological networks such as metabolic, cell signaling or transcriptional regulatory networks are intrinsically directional, and using metrics that ignore edge direction may gravely hinder information extraction. The applicability of graphlets is extended to directed networks by considering the edge direction of the graphlets. We tested our approach on a set of directed biological networks and verified that they were correctly grouped by type using directed graphlets. However, enumerating all graphlets in a large network is a computationally demanding task. Our implementation addresses this concern by using a state-of-the-art data structure, the g-trie, which is able to greatly reduce the necessary computation. We compared our tool, gtrieScanner, to other state-of-the art methods and verified that it is the fastest general tool for graphlet counting.

Motivation & Objective

• To address the limitation of undirected graphlets in capturing directional topological features in biological networks such as metabolic, signaling, and regulatory networks.
• To develop a scalable and efficient method for enumerating directed graphlets of arbitrary size, overcoming computational bottlenecks in large network analysis.
• To enable accurate network comparison and classification by type using directed graphlets, leveraging edge direction for improved structural insight.
• To create a general-purpose tool that supports both graphlet and network motif enumeration with customizable subgraph queries.

Proposed method

• Extends the graphlet framework to directed networks by considering edge direction in subgraph isomorphism, enabling the identification of directed graphlets as non-isomorphic directed subgraphs.
• Employs the g-trie data structure to compactly represent and efficiently enumerate all possible graphlets up to a given size, significantly reducing redundant computation.
• Uses a recursive equation system to compute higher-order graphlet frequencies from lower-order ones, minimizing repeated traversal of the network.
• Implements a flexible query interface allowing users to specify custom sets of graphlets or motifs for analysis, enhancing tool adaptability.
• Optimizes performance by leveraging the g-trie’s ability to index and traverse subgraph patterns efficiently, especially in large networks.
• Supports both undirected and directed graphlets, as well as network motifs, with a single unified framework and implementation.

Experimental results

Research questions

• RQ1 Can directed graphlets effectively distinguish between different types of biological networks, such as metabolic, signaling, and transcriptional regulatory networks?
• RQ2 How does the inclusion of edge direction in graphlet analysis improve the detection of structural differences compared to undirected graphlets?
• RQ3 To what extent can the g-trie data structure accelerate graphlet enumeration in large directed networks compared to existing tools?
• RQ4 How does gtrieScanner compare in performance to state-of-the-art tools for graphlet and network motif enumeration across various network types and sizes?

Key findings

• Directed graphlets successfully grouped biological networks by type, demonstrating their ability to capture meaningful topological differences that undirected graphlets miss.
• gtrieScanner achieved an average speedup of nearly two orders of magnitude over network motif tools (e.g., Kavosh, FANMOD) for undirected graphs and about 20× speedup for directed graphs.
• The tool outperformed GraphCrunch and ORCA, which are limited to undirected graphlets of size ≤5, by supporting larger and directed graphlets.
• gtrieScanner is the fastest general-purpose tool for graphlet and motif counting, with superior scalability and flexibility for arbitrary subgraph queries.
• The use of recursive equations based on g-trie indexing reduced computational overhead, especially for larger graphlets, without sacrificing accuracy.
• The method enables efficient analysis of directed networks such as transcriptional regulatory and signaling pathways, where edge direction carries critical biological meaning.