Graph Traversal & Pathway Interrogation

AA large, densely cross-linked site has more potential connections between articles than any reader can hold in their head. The value of turning that into an actual graph, rather than leaving it as an implicit similarity table, is that well-understood graph algorithms then do the work of finding a route: shortest-path search doesn't just tell a reader that two articles are related, it tells them the cheapest sequence of intermediate stops and, via the bridge-term interrogation below, what each stop actually contributes to the journey. The trade-off is the one every road network faces: capping degree and proximity keeps the map legible, but it also means the "true" nearest neighbour in high-dimensional embedding space is sometimes not directly reachable by a single road, and has to be approached by a short hop through a waystation instead — which is itself a more honest picture of how ideas actually connect than a single straight line would be.

The Local k-NN Spatial Highway Graph

EarlyEarly 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 neighbours 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

WhenWhen a reader hovers over a destination node on the Concept Atlas map, the frontend pathfinder executes a Breadth-First Search (BFS) or Dijkstra algorithm[2] 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

BeyondBeyond 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:

Interactive Road Polylines

InIn 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.

This pairing of graph search with mid-edge vector interrogation is what separates the Concept Atlas from a conventional "related articles" widget. A similarity list can tell a reader that two pages are related; it can't tell them why, because the relationship exists only as a number, not as anything inspectable along the way. Treating each road as a real edge with a real midpoint — a point that itself sits somewhere in the underlying vector space, with its own nearest vocabulary terms — turns an opaque distance metric into a small, explicit vocabulary of transitional concepts a reader can read before committing to the jump. It's a deliberately cheap technique: no separate explanation-generation step, just a second lookup against the same weight space the layout is already built from.

References

1. Hart, P. E., Nilsson, N. J., and Raphael, B., "A Formal Basis for the Heuristic Determination of Minimum Cost Paths," IEEE Transactions on Systems Science and Cybernetics, vol. 4, no. 2, pp. 100–107, 1968. https://doi.org/10.1109/TSSC.1968.300136
2. Dijkstra, E. W., "A note on two problems in connexion with graphs," Numerische Mathematik, vol. 1, pp. 269–271, 1959. https://doi.org/10.1007/BF01386390