Extending the Applicability of Graphlets to Directed Networks

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 analyzing 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 due to the rich topological information that they offer 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. Our main purpose in this work is to extend the applicability of graphlets to directed networks by considering their edge direction, thus providing a powerful basis for the analysis of directed biological networks. We tested our approach on two network sets, one composed of synthetic graphs and another of real directed biological networks, and verified that they were more accurately grouped using directed graphlets than undirected graphlets. It is also evident that directed graphlets offer substantially more topological information than simple graph metrics such as degree distribution or reciprocity. However, enumerating graphlets in large networks 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 to other state-of-the art methods and verified that it is the fastest general tool for graphlet counting.

Graphlet-based Characterization of Directed Networks

“…Research on uncovering their organizational principles and function will continue. Applying our new directed graphlet-based methods, or devising new methods for their analyses 62 63 are a subject of future research.…”

A Survey on Subgraph Counting: Concepts, Algorithms and Applications to Network Motifs and Graphlets

“…However, since this data-structure encapsulates the information of multiple graphs in an hierarchical order, it achieves a much faster full subgraph counting algorithm. The usage of this data-structure has been significantly extended since its original publication, such as a version for colored networks [148] or an orbit aware version [13]. A more detailed discussion of the data-structure and the subgraph counting algorithm is presented in [149].…”

GoT-WAVE: Temporal network alignment using graphlet-orbit transitions

“…In directed graphs, edges (i, j) are ordered pairs (translated to "i goes to j"), whereas in undirected graphs there is no order since nodes are always reciprocally connected. Our proposed methodology (see below) is applicable to both undirected and directed graphs [2]. A temporal network comprises s consecutive network snapshots.…”