Regular Equivalence Role Assigner Tool

Compute coarsest seed-refining directed regular-role partition by distinct outgoing/incoming neighbor-role sets, not neighbor counts. Bounded finite refinement, deterministic first-node labels; not unconstrained latent social-role or structural-equivalence inference.

Description

Network role refinement groups nodes by the role types they reach and receive ties from.

Network role refinement groups nodes by the role types they reach and receive ties from.^[1]

The declared seed partition constrains the refinement and differs from automatically discovering one unique sociological role system.

When to use Regular Equivalence Role Assigner Tool

Use this tool to obtain refinedRoleIds, refinedRoleCount from the supplied records using the stated calculation. Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.

How to use Regular Equivalence Role Assigner Tool and understand its results

Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
Enter observedDirectedAdjacency, callerSeedRoleIds, using the field meanings and rules below, then run the tool.
Read result.refinedRoleIds, result.refinedRoleCount. Use the units and sign conventions below, and review any unknown records separately.
Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.

Input field	Meaning	Value type	Requirement
observedDirectedAdjacency	Observed directed adjacency	numeric matrix	Required
callerSeedRoleIds	Caller seed role ids	list of number	Required

Require a binary directed square adjacency matrix for two through 32 nodes with no self-loops, and aligned integer seed role IDs from zero through 31. For each node form a signature from its current role, sorted unique outgoing-neighbor roles and incoming-neighbor roles. Reassign signature IDs in first-appearance order and repeat until pairwise partition membership stabilizes or at most n rounds. Return refined IDs and class count. Multiplicity is ignored in signatures, and seed classes are not merged.

signature_i=[role_i,uniqueSorted(outgoingRoles_i),uniqueSorted(incomingRoles_i)]; nextRole_i=firstAppearanceIndex(signature_i)

Use the matching field units and the exact boundary, ordering and reference rules above.

Output field	Meaning	Value type
result	Calculated observation or qualified reference	object
result.refinedRoleIds	Refined role classes aligned with graph nodes; IDs follow signature first appearance.	list
result.refinedRoleCount	Number of distinct classes in the returned refined partition.	number

json

{
  "input": {
    "observedDirectedAdjacency": [
      [
        0,
        1,
        0
      ],
      [
        1,
        0,
        1
      ],
      [
        0,
        1,
        0
      ]
    ],
    "callerSeedRoleIds": [
      0,
      0,
      1
    ]
  },
  "output": {
    "result": {
      "refinedRoleIds": [
        0,
        1,
        2
      ],
      "refinedRoleCount": 3
    }
  }
}

Limitations and assumptions

Population definitions, survey design, calibration and observation coverage are independently established. A result describes the supplied record or conditional model without demonstrating causation, validating an instrument or supplying representative population evidence.

Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries, subject to the narrower lengths and code rules above. Numeric matrices allow at most 128 rows and 128 columns, subject to the narrower shape requirements above. Extremely large composite outputs are rejected.

Alternative or Complementary methods

For a related step, use Core-Periphery Fit Index Calculator: An ideal core-periphery comparison tests a declared core partition against observed ties. For a complementary comparison, use Blockmodel Image Matrix Density Calculator: A blockmodel image can summarize directed edge density between declared node groups.

References

Regular Equivalence Role Assigner Tool — tool.io

Similar or alternative tools

Core-Periphery Fit Index Calculator
An ideal core-periphery comparison tests a declared core partition against observed ties.
Blockmodel Image Matrix Density Calculator
A blockmodel image can summarize directed edge density between declared node groups.