Directed Graph Triangle Counting With Tagged Edge Directionality
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Solution Overview
Problem
Existing triangle count methods for graph structure data are inefficient for directed graphs, leading to redundant calculations due to counting triangles multiple times, especially for vertices with many neighbors, and do not account for edge directionality.
Innovation Solution
A method for processing directed graphs by representing directed edges in a unified form and generating tagged edges to record original edge directions, allowing for accurate triangle category identification and feature vector generation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional triangle count methods are applied to directed graphs, then triangle counting can be performed, but redundant calculations occur and computing resources are wasted
Solution Approach 1:
The patent segments the triangle counting process by introducing tagged edges that categorize different triangle types (e.g., cyclic triangles, transitive triangles) based on edge directionality. This segmentation allows the algorithm to process different triangle categories separately, avoiding redundant calculations across all vertices.
Solution Approach 2:
The patent performs preliminary action by pre-tagging edges with directionality information before the triangle counting process. This preliminary tagging enables the algorithm to identify and skip certain triangle configurations that would otherwise require full processing, thereby reducing redundant computations.
2Measurement precision
If triangle counting is performed for each vertex in the graph, then complete triangle identification is achieved, but each triangle is counted three times causing considerable redundant calculations
Solution Approach 1:
The patent introduces asymmetry by using directed edges with specific directionality tags instead of treating all edges symmetrically. This asymmetric approach allows the algorithm to establish a unique ordering for triangle identification, ensuring each triangle is counted exactly once rather than three times.
Solution Approach 2:
The patent inverts the traditional approach by instead of counting all triangles from each vertex, it uses the tagged edge directions to determine a canonical representation of each triangle, counting it only from the appropriate starting vertex based on the inversion of the counting logic.
3Device complexity
If edge directionality is not considered in triangle counting, then simpler algorithms can be used, but triangle categories caused by directionality cannot be identified
Solution Approach 1:
The patent introduces tagged edges as an intermediary element that carries directionality information without complicating the core triangle counting logic. These tags act as mediators that preserve edge directionality information while enabling the algorithm to proceed with modified but not excessively complex processing.
Solution Approach 2:
The patent changes the parameter representation by adding directional tags to edges, transforming the graph representation from simple adjacency to tagged adjacency. This parameter change enables the algorithm to distinguish edge directions and identify triangle categories without requiring a complete redesign of the counting mechanism.
Data Source
AI summary
A graph data processing method includes acquiring a directed graph, where a directed edge in the directed graph is represented as pointing to a destination vertex from a start vertex; representing the directed edge in a unified form according to a specified order between a vertex identifier of the start vertex and a vertex identifier of the destination vertex; generating a tagged edge for recording an original edge direction of the directed edge, to obtain a tagged directed graph; and identifying a category of a triangle constituted by a vertex in the tagged directed graph, a neighbor vertex of the vertex, and a common vertex commonly adjacent to the vertex and the neighbor vertex, based on tagged edges between two of the vertex, the neighbor vertex, and the common vertex.