Harmonic evolutions on graphs
arXiv:1201.1355
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.
16 pages, 7 figures