isomorphism

Examples of isomorphism in the following topics:

• Introduction to finding equivalence Sets

  • When the new graph and the old graph have the same distances among nodes, the graphs are isomorphic, and the "swapping" that was done identifies the isomorphic sub-graphs.
  • One approach to binary data, "all permutations," (Network>Roles & Positions>Automorphic>All Permutations) literally compares every possible swapping of nodes to find isomorphic graphs.

• Defining automorphic equivalence

  • Formally "Two vertices u and v of a labeled graph G are automorphically equivalent if all the vertices can be re-labeled to form an isomorphic graph with the labels of u and v interchanged.

• All permutations (i.e. brute force)

  • The isomorphism classes that it located are called "orbits."

• Equivalence of distances: Maxsim

  • Mathematically, this is a sensible result; exchanges of labels of actors within these sets can occur and still produce an isomorphic distance matrix.

• Analogies

  • The concepts of association, comparison, correspondence, mathematical and morphological homology, homomorphism, iconicity, isomorphism, metaphor, resemblance, and similarity are closely related to analogy.