Keywordsgraph theory; applications of graph theory; group theory fuzzy sets; fuzzy logic; logic of vagueness; fuzzy topology; Fuzzy Measure theory; fuzzy real analysis; Small World graphs; Complex Networks; artificial intelligence; heat semigroup; Haar distribution; path group; independent set; independence polynomial; symmetric polynomial; palindromic polynomial; mathematical analysis; measure theory; fuzzy systems; information theory; information theory; networks; quantitative graph analysis; asynchronous system; symmetry; semi-regularity