Graph Traversal & Pathway Interrogation

Graph Theory & Semantic Highways

This article details how the Concept Atlas constructs a local k-Nearest-Neighbors (k-NN) road network and performs shortest-path graph search (BFS/A*) to connect articles. Learn how intermediate neuron weight vectors are interrogated to discover transitional "bridge concepts" along travel routes.

The Local k-NN Spatial Highway Graph

Early cartographic web prototypes constructed road lines based on global document hyperlinks or raw Euclidean distance across the map. However, drawing long diagonal lines across the canvas creates visual clutter and obscures terrain features. To solve this, the road network is constructed using a Local k-Nearest-Neighbors (k-NN) Spatial Graph:

  • Maximum Proximity Bound: Roads are only created between spatial neighbors within a radius of 7.5 hex grid units.
  • Degree Capping: Each node is capped at a maximum of 3 outgoing road connections to ensure clean, readable highways.
  • Terrain Following: Road polylines follow low U-Matrix valleys, avoiding steep mountain ridges wherever possible.

Graph Pathfinding & Route Traversal

When a reader hovers over a destination node on the Concept Atlas map, the frontend pathfinder executes a Breadth-First Search (BFS) or Dijkstra algorithm over the adjacency graph connecting "YOU ARE HERE" to the target node:

[YOU ARE HERE: Risk Management]
        │ (Road 1: Bridge Concepts: "Security", "Compliance")
        ▼
[Waystation 1: Legal Framework in Computing]
        │ (Road 2: Bridge Concepts: "Contracts", "Specification")
        ▼
[TARGET: Project Marking as BDD]

As the algorithm steps through the road network graph, it accumulates intermediate node titles, road segment bridge terms, and target node concepts into a unified route summary displayed in the inspection banner.

SOM Weight Vector Bridge Interrogation

Beyond simple graph traversal, the SOM Atlas interrogates the high-dimensional weight vectors at the exact midpoint hex of every road segment. By comparing the neuron vector $W_{\text{mid}}$ against the vocabulary term dictionary, the generator extracts the top transitional terms that bridge two distinct articles:

Example Bridge Interrogation:

Connecting Chatbots in Healthcare to Legal Framework in Computing yields transitional bridge concepts: Privacy • Governance • Liability • Data Protection.

Interactive Road Polylines

In SVG rendering, thin 3px road polylines can be difficult to target with a mouse cursor. To ensure effortless user interaction, each road segment is rendered inside an invisible 16px transparent hit area group (<g class="atlas-road-group">). Hovering anywhere near a road line highlights the pathway and displays its bridge concepts in the inspection banner.