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We introduce a definition of algorithmic symmetry able to capture essentialaspects of geometric symmetry. We review, study and apply a method forapproximating the algorithmic complexity (also known as Kolmogorov-Chaitincomplexity) of graphs and networks based on the concept of AlgorithmicProbability (AP). AP is a concept (and method) capable of recursivelyenumeration all properties of computable (causal) nature beyond statisticalregularities. We explore the connections of algorithmic complexity---boththeoretical and numerical---with geometric properties mainly symmetry andtopology from an (algorithmic) information-theoretic perspective. We show thatapproximations to algorithmic complexity by lossless compression and anAlgorithmic Probability-based method can characterize properties ofpolyominoes, polytopes, regular and quasi-regular polyhedra as well aspolyhedral networks, thereby demonstrating its profiling capabilities.

Symmetry and Algorithmic Complexity of Polyominoes and Polyhedral Graphs