Harmonic evolutions on graphs
Jerzy Kocik
TL;DR
This paper introduces harmonic evolution on graphs using the Laplacian over Z_2, offering a novel geometric perspective and a new analytical tool, with classification of evolution digraphs and a connection to cellular automata.
Contribution
It defines harmonic evolution on graphs via the Laplacian over Z_2, providing a new geometric framework and classification method for graph evolutions.
Findings
Classified digraphs of harmonic evolutions
Established a topological generalization of cellular automata
Provided a new analytical tool for graph analysis
Abstract
We define the harmonic evolution of states of a graph by iterative application of the harmonic operator (Laplacian over ). This provides graphs with a new geometric context and leads to a new tool to analyze them. The digraphs of evolutions are analyzed and classified. This construction can also be viewed as a certain topological generalization of cellular automata.
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Taxonomy
TopicsCellular Automata and Applications · Markov Chains and Monte Carlo Methods · Graph theory and applications