Network positions and social roles: The idea of equivalence

1. Network positions and social roles: The idea of equivalence Liqiong Liu

2. Contents • I Approach to define • II Defining equivalence or similarity • ❍ Structural equivalence • ❍ Automorphic equivalence • ❍ Regular equivalence • III Automorphic equivalence • IV Empirical research

3. I Purpose • To describe social roles and social positions • To understand or predict social behavior • Working class, middle class, upper class • Income • Consumption of Luxury

4. I Approach • Based on Attributes of individual actors • European-American males, ages 45-64 are likely to have relatively high incomes • Based on similarities of the patterns of relations among actors • husband, wife, child • White,non-whites

5. II Defining equivalence or similarity • ❍ Structural equivalence • ❍ Automorphic equivalence • ❍ Regular equivalence A C B D E F G H I

6. II Distinction

7. III Automorphic equivalence • ❍ All permutations (i.e. brute force) Network>Roles & Positions>Automorphic>All Permutations • ❍ Optimization by tabu search Network>Roles & Positions>Exact>Optimization • ❍ Equivalence of distances: MaxsimNetwork>Roles & Positions>Automorphic>MaxSim

8. All permutations

9. Optimization by tabu search

10. Equivalence of distances: Maxsim

12. IV Empirical research