isomorphism

(noun)

A one-to-one correspondence.

Related Terms

  • homomorphism
  • iconicity

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.
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