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--- retegraphprocessing:elements:prototyping:simple_algorithm [2023/06/12 05:21] – gedbadmin
+++ retegraphprocessing:elements:prototyping:simple_algorithm [2024/01/19 17:41] (current) – removed gedbadmin
@@ Line 1: / Line 1: @@
-====== Simple Algorithm Prototype ======
-The goal of this prototype is to implement a simple algorithm for detecting simple cycles within a graph.
-Let //G = (V,E)// be a directed graph (//G//) consists of a finite set of vertices (//V//) and a finite set of edges (//E//).  Each edge describes a relationship v<sub>1</sub> -> v<sub>2</sub> where v<sub>1</sub> and v<sub>2</sub>  are distinct members of V.
-Within G a cycle of length //l// is a sequence of vertices [v<sub>0</sub>,v<sub>1</sub>,...,v<sub>//l//</sub>] where v<sub>//i//]-1</sub> -> <sub>//i//]</sub> for i = 1, 2, ...., //l//-1 and v<sub>//l//</sub> -> v<sub>1</sub>.
-The cycle is simple when each vertex in [v<sub>0</sub>,v<sub>1</sub>,...,v<sub>//l//</sub>] are destinct, so that v<sub>//i//</sub> ≠ v<sub>//j//</sub> for //i// ≠ //j//.
-====== References ======
-* Golumbic, M. C. (2004). Algorithmic Graph Theory and Perfect Graphs (2nd ed., Chapter 1 - Graph Theoretic Foundations). North Holland Publishing Company, a Subsidiary of Eslevier.