Urbanization Driver Implication Chain Builder

Trace all drivers reachable from a selected root in a caller-supplied binary driver-link matrix.

Description

A driver graph records directed implications.

A driver graph records directed implications. Reachability identifies which listed drivers can be reached from a chosen root.^[1]

The returned values include Unreachable drivers, Reachable drivers, Reachable driver IDs, Root reaches all drivers. The How section below explains the calculation, input rules and interpretation.

When to use Urbanization Driver Implication Chain Builder

Use Urbanization Driver Implication Chain Builder when you need to evaluate the supplied records under the calculation and evidence rules below. Links are caller assumptions, not proven causal effects. Cycles do not make traversal infinite.

Define the question, evidence and scenario assumptions first. Supply the chosen score scales, time horizons or reference selection explicitly. Interpret generated text as a discussion template and screen labels as the stated rules.

How to use Urbanization Driver Implication Chain Builder and understand its results

Define the question, evidence and scenario assumptions first. Supply the chosen score scales, time horizons or reference selection explicitly. Interpret generated text as a discussion template and screen labels as the stated rules.
Enter driverIds, links, rootDriverId using the field table and calculation rules, then run the tool.
Read disconnectedDriverIds, reachableCount, reachableDriverIds, rootReachesAllDrivers. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
driverIds	Driver IDs	list of string	Required
links	Square directed-link matrix with binary values.	list of list of number	Required
rootDriverId	Root driver ID	string	Required

Trim nonblank IDs/root, require root to match a listed ID and a square binary matrix. Traverse rows to outgoing columns in index order, include root, avoid revisiting indexes and return traversal-order IDs plus disconnected IDs in input order. Duplicate IDs are allowed; root uses first match.

reachable=breadthFirstTraversal(root, binary adjacency matrix)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
disconnectedDriverIds	Unreachable drivers	list of string
reachableCount	Reachable drivers	integer; minimum: 1
reachableDriverIds	Reachable driver IDs	list of string
rootReachesAllDrivers	Root reaches all drivers	boolean

json

{
  "input": {
    "driverIds": [
      "Migration",
      "Housing",
      "Transit",
      "Jobs"
    ],
    "links": [
      [
        0,
        1,
        1,
        0
      ],
      [
        0,
        0,
        0,
        1
      ],
      [
        0,
        0,
        0,
        1
      ],
      [
        0,
        0,
        0,
        0
      ]
    ],
    "rootDriverId": "Migration"
  },
  "output": {
    "disconnectedDriverIds": [],
    "reachableCount": 4,
    "reachableDriverIds": [
      "Migration",
      "Housing",
      "Transit",
      "Jobs"
    ],
    "rootReachesAllDrivers": true
  }
}

Limitations and assumptions

Links are caller assumptions, not proven causal effects. Cycles do not make traversal infinite.

Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Core numeric and string lists are limited to 100,000 entries; text entries are subject to the general large-text limit. Follow any smaller calculation limits above. Matrices are limited to 128 rows and 128 entries per row. Extremely large text inputs are rejected. Missing fields without a declared default, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use Digitalization Acceleration Driver Tree: A digitalization driver tree connects each node with one parent. A valid tree needs one root and no parent cycle. For a complementary task, use Cross Impact Analysis Event Pair Matrix: Cross-impact matrices distinguish directed relationships between events. Positive and negative scores need separate interpretation.

References

Urbanization Driver Implication Chain Builder — tool.io

Similar or alternative tools

Digitalization Acceleration Driver Tree
A digitalization driver tree connects each node with one parent. A valid tree needs one root and no parent cycle.
Cross Impact Analysis Event Pair Matrix
Cross-impact matrices distinguish directed relationships between events. Positive and negative scores need separate interpretation.