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#graph neural networks Open access

KHANH MATHEMATICS - Chapter 2: Directed Graphs for AI, Knowledge Graphs & Neural DAGs: From Basics of Directed Graphs (Lecture 6, 2012) to Deep-Tech Graph Systems 2026

Kim Khanh Nguyen
Oct 2026 · Zenodo (CERN European Organization for Nuclear Research)
Graph Theory and Algorithms

Abstract

KHANH MATHEMATICS - Chapter 2: Directed Graphs for AI, Knowledge Graphs & Neural DAGs Author: Nguyen Kim KhanhAffiliation: Khanh UniversityORCID: 0009-0006-9191-1441Email: khanhtbys@gmail.comDate: 20 Oct 2026, Ho Chi Minh City, Vietnam Abstract:This chapter reconstructs Lecture 6 (Basics of Directed Graphs, Definition 6.1) from Lectures on Discrete Mathematics for Computer Science (Khoussainov & Khoussainova, World Scientific 2012, ISBN 978-981-4340-50-2). Original definition: A digraph consists of vertices (points) and edges (directed lines), V denotes vertices, E edges, with example V={0,1,2,3,4,5,6,7,8,9} on page 49. We extend it to modern applications: Knowledge Graphs (including Toan Hoc Khanh 61-member network), Neural Network Computational DAGs, Blockchain DAGs (GHOST, PHANTOM, GHOSTDAG), and path problems for AI reasoning. Covers reachability, adjacency matrix, Warshall O(n^3), topological sort, DAG longest path, and connection to Chapter 1's integer properties (A^k counts paths). This is the direct sequel to Chapter 1: Number Theory for Deep-Tech (published 10:34 today). Keywords: directed graphs, digraphs, DAG, topological sort, path problem, knowledge graphs, neural DAGs, blockchain DAG, GHOST, discrete mathematics, Khanh Mathematics License: CC BY 4.0 SOLI DEO GLORIA.AD MAIOREM DEI GLORIAM IN SAECULA SAECULORUM. Related identifiers: Link to Chapter 1 DOI (isSupplementTo / isContinuedBy)

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