Fig 1.
The collection of all triad types (triad census).
The labels consist of three digits: the first digit denotes the number of mutual links (↔), the second stands for the number of arcs (→) while the third denotes the number of missing links between two units. Some types of triads with the same distribution of links are further differentiated (see columns) and labeled with a letter (C stands for cycle, T for transitivity, U for up and D for down).
Fig 2.
Cohesive blockmodel with different level of errors.
(A) level of errors is 0 (ideal blockmodel), (B) level of errors is 0.25, (C) level of errors is 0.50, (D) level of errors is 1 (random network).
Fig 3.
Different types of blockmodel structures: Graph (left) and matrix (right) representation.
(A) cohesive, (B) symmetric core-periphery, (C) asymmetric core-periphery, (D) hierarchical without complete blocks on the diagonal, (E) hierarchical with complete blocks on the diagonal, (F) transitive without complete blocks on the diagonal, (G) transitive with complete blocks on the diagonal; gray colored cells denote complete blocks while white colored cells denote null blocks.
Table 1.
A-measure values and the classification of allowed and forbidden triad types, and selected allowed and forbidden triad types for different types of blockmodels.
Values greater than zero denote allowed types of triads while the values which equals zero (cells without numbers) denotes forbidden types of triads; grey color denotes selected triad types.
Fig 4.
The MIV for each blockmodel type (generated by the RL algorithm) and selected set of triad types.
(A) cohesive; (B) symmetric core-periphery; (C) asymmetric core-periphery; (D) hierarchical without complete blocks on the diagonal (E) hierarchical with complete blocks on the diagonal; (F) transitivity without complete blocks on the diagonal; (G) transitivity with complete blocks on the diagonal, (1) allowed and forbidden triad types, (2) allowed triad types, (3) forbidden triad types. Note: only networks of transitivity with complete blocks on the diagonal blockmodel type and hierarchical with complete blocks on the diagonal blockmodel type were generated by considering the selected allowed triad types.
Fig 5.
Some generated networks with the expected hierarchical blockmodel without complete blocks on the diagonal.
The RL algorithm is used and all triad types are considered.
Fig 6.
The MIV for each blockmodel type (generated by the MCMC algorithm with fixed density) and selected set of triad types.
(A) cohesive; (B) symmetric core-periphery; (C) asymmetric core-periphery; (D) hierarchical without complete blocks on the diagonal (E) hierarchical with complete blocks on the diagonal; (F) transitivity without complete blocks on the diagonal; (G) transitivity with complete blocks on the diagonal, (1) allowed and forbidden triad types, (2) allowed triad types, (3) forbidden triad types. Note: only the networks of transitivity with complete blocks on the diagonal blockmodel type and hierarchical with complete blocks on the diagonal blockmodel type were generated by considering the selected allowed triad types.
Fig 7.
Some empirical generated networks using the RL algorithm by considering all triad types.
By rows: (A) cohesive; (B) symmetric core-periphery; (C) asymmetric core-periphery; (D) hierarchical without complete blocks on the diagonal; (E) hierarchical with complete blocks on the diagonal; (F) transitivity without complete blocks on the diagonal; (G) transitivity with complete blocks on the diagonal.
Fig 8.
The MIV for each blockmodel type (generated by the MCMC algorithm with variable density) and selected set of triad types.
(A) cohesive; (B) symmetric core-periphery; (C) asymmetric core-periphery; (D) hierarchical without complete blocks on the diagonal (E) hierarchical with complete blocks on the diagonal; (F) transitivity without complete blocks on the diagonal; (G) transitivity with complete blocks on the diagonal, (1) allowed and forbidden triad types, (2) allowed triad types, (3) forbidden triad types. Note: only the networks of transitivity with complete blocks on the diagonal blockmodel type and hierarchical with complete blocks on the diagonal blockmodel type were generated by considering the selected allowed triad types.
Fig 9.
Some generated networks with a hierarchical blockmodel structure without complete blocks on the diagonal using different models.
The networks are generated by the MCMC algorithm with a non-fixed density. (a) All selected types of triads; (b) All selected types of triads and paths of length three; (c) All selected types of triads (with a higher parameter value for the triad of type 021D) and paths of length three.
Fig 10.
Some examples of generated networks for each type of a blockmodel.
The networks are generated using the RL algorithm by selected allowed types of triads. (A) cohesive; (B) symmetric core-periphery; (C) asymmetric core-periphery; (D) hierarchical without complete blocks on the diagonal (E) hierarchical with complete blocks on the diagonal; (F) transitivity without complete blocks on the diagonal; (G) transitivity with complete blocks on the diagonal.