Blockmodel Image Matrix Density Calculator

Actual directed blockmodel density under independent block assignments, self-loops excluded. No eligible dyad returns0by explicit empty-cell convention, not inferred equivalence or latent community detection.

Description

A blockmodel image can summarize directed edge density between declared node groups.

A blockmodel image can summarize directed edge density between declared node groups.^[1]

Within-block possibilities exclude self-loops, while singleton diagonal cells have no possible ties.

When to use Blockmodel Image Matrix Density Calculator

Use this tool to obtain blockIds, observedBlockDensityMatrix 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 Blockmodel Image Matrix Density Calculator and understand its results

Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
Enter observedDirectedAdjacency, callerBlockAssignments, using the field meanings and rules below, then run the tool.
Read result.blockIds, result.observedBlockDensityMatrix. 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
callerBlockAssignments	Caller block assignments	list of string	Required

Require a binary directed zero-diagonal graph for two through 32 nodes and aligned nonblank block labels. Keep block IDs in first-appearance order. For each ordered block pair count observed arcs and possible non-self ordered pairs, then divide. A cell with no possible pairs returns zero, including a singleton within-block cell. No automatic block assignment or binary image threshold is supplied.

density_ab=arcs(fromBlock=a,toBlock=b)/possibleNonSelfOrderedPairs_ab, or 0 when none possible

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.blockIds	Distinct supplied block labels in first-appearance order.	list
result.observedBlockDensityMatrix	Directed edge densities by ordered block pair, with rows and columns aligned to blockIds.	list

json

{
  "input": {
    "observedDirectedAdjacency": [
      [
        0,
        1,
        0
      ],
      [
        0,
        0,
        1
      ],
      [
        1,
        0,
        0
      ]
    ],
    "callerBlockAssignments": [
      "a",
      "a",
      "b"
    ]
  },
  "output": {
    "result": {
      "blockIds": [
        "a",
        "b"
      ],
      "observedBlockDensityMatrix": [
        [
          0.5,
          0.5
        ],
        [
          0.5,
          0
        ]
      ]
    }
  }
}

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. String lists allow at most 128 entries of at most 128 UTF-16 units each; blank and duplicate rules are stated 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 Regular Equivalence Role Assigner Tool: Network role refinement groups nodes by the role types they reach and receive ties from. For a complementary comparison, use Core-Periphery Fit Index Calculator: An ideal core-periphery comparison tests a declared core partition against observed ties.

References

Blockmodel Image Matrix Density Calculator — tool.io

Similar or alternative tools

Regular Equivalence Role Assigner Tool
Network role refinement groups nodes by the role types they reach and receive ties from.
Core-Periphery Fit Index Calculator
An ideal core-periphery comparison tests a declared core partition against observed ties.