Egress as a Graph

Ask how far someone has to walk to get out of a floor and the tempting answer is a ruler: measure from the far room to the nearest exit door. Wrong measurement. Nobody leaves a building in a straight line. They leave through a door, down a corridor, around the core and past every wall the ruler went straight through. Travel distance is the length of the route, and the route is always at least as long as the line — sometimes much longer, and sometimes it doesn’t exist at all.

A straight line is not a route

Six room-center nodes connect to a 48 ft deep schematic corridor plan. Walking weights use 14 ft room-center links and measured horizontal centerline lengths. The straight line runs from the selected room center to the nearest active exit and ignores walls and connections. The result is a graph path, not a full egress or travel-distance review.

The plan as a graph

Egress can be modeled as a graph: rooms and decision points are nodes, doors and corridors are connections, and exits are destinations. Travel distance is the length of a route through that graph. An exit’s presence alone is not enough; occupants need a usable path to reach it.

Quick glossary. A node is a place. An edge is a walkable connection between two places, and its weight is the walking distance along it. The shortest path from a room to an exit is the chain of connected edges with the smallest total weight. Finding it is a solved problem — Dijkstra’s algorithm, which is what both the original April applet and the rebuilt drawing on this page run. The hard part was never the math. It’s that a drawing made of lines doesn’t know which lines you can walk through.

Two distances for the same room

The drawing is a schematic 90 ft × 48 ft floor: three rooms on each side of a central corridor, with a possible exit at each end. Each room joins the corridor by a 14 ft link from its center to the corridor centerline, landing 15, 45 or 75 ft along it. The orange line is the walked route the graph finds. The dashed gold line is the straight line to the nearest active exit, the thing a ruler (or a heat map) measures. Here is one room, R6 in the lower right, through four presets:

• Only the left exit. The straight line from R6’s center to the left exit runs 75 ft across and 14 ft down: √(75² + 14²) = 76.3 ft. The route is 14 ft out to the corridor plus 75 ft along it: 89 ft. Same room, same exit, 12.7 ft apart. In a plan this simple the route is just the two legs of the triangle and the line is its hypotenuse, so the gap is modest.
• Block one corridor segment. Cut the 30 ft run between the first and middle corridor stops. The straight line is still 76.3 ft — nothing about the ruler measurement changed. The route is gone. R6 has no connected path to an exit, and neither do R2, R3 or R5: two of six rooms can still get out. A straight-line check scores this plan exactly the same as the last one.
• Turn the right exit back on. R6’s route drops to 29 ft (14 + 15) against a 20.5 ft straight line, and all six rooms have a path again. The worst-served rooms are now the middle pair, R2 and R5, at 59 ft. The second exit didn’t shorten anyone’s walk to the first one. It supplied a different route.
• Stretch the corridor to 138 ft, left exit only. R3, at the far end, walks 129 ft against a 115.8 ft straight line. The gap barely moves, to 13.2 ft, because the only detour in this plan is the 14 ft link. A straight corridor keeps the two numbers close; turns, dead ends and blocked segments are what pull them apart.

That is the whole distinction. The straight line is a floor: the route can never be shorter. But it can be any amount longer, and the straight line can’t see a blocked corridor, a locked door or a wall at all. Use it as a quick first pass if you like. Don’t mistake it for travel distance.

This is the mistake Portal V made a day earlier. Its heat map measured straight lines from sample points to the nearest exit across an empty rectangle and labeled the result travel distance. Its corrected edition sends readers here because this is where distance is finally measured along the path.

There is no one number

Editorial note, added October 15, 2026. As published on June 19, 2026, this page said IBC travel-distance limits are “200 feet for sprinklered buildings and 75 feet for unsprinklered in most occupancy types,” and the original applet still checks every route against a fixed 200 ft. That claim is withdrawn, the same way Portal V’s single 200 ft cap was. No single number is the rule — even my own notes disagree, since Thesis #22 gives a 100-foot maximum. The applicable limit depends on the occupancy, whether the building is sprinklered, and the code the jurisdiction actually adopted, with its amendments. The common-path and exit-separation figures the April version gave are cut for the same reason rather than restated. Read the original applet’s “COMPLIANT” and “VIOLATION” labels as a comparison against 200 ft, not a code verdict.

The rebuilt drawing draws no limit line at all. It reports route lengths and leaves the comparison to whoever knows which code applies.

Two more graph questions

Two other graph questions matter. How far must someone travel before reaching a point with two directions of egress? And are the exits separated enough that one event is less likely to block both? A long dead-end segment or a pair of nearby exits can weaken those alternatives even when the plan has the required count.

Both read straight off the graph. The first is the length of the route before it branches. In the drawing, with both exits on, every room reaches a branch where its link meets the corridor, 14 ft from its center; with only the left exit, R6’s entire 89 ft walk is a single direction with nowhere else to go. The second asks whether two routes diverge early enough that one blockage can’t cut both. The drawing’s exits sit at opposite ends of the corridor, which is why blocking one segment strands nobody while both are open. Put the two exits side by side at one end and a single blocked segment would cut off everything beyond it. Same exit count, very different graph.

Measure along the path

The graph helps locate layout questions for review. Applicable travel, common-path, and exit-separation limits vary with occupancy and adopted code, so the simplified path model does not establish compliance.

What it does establish is which distance to hand the reviewer. A plan tool that stores doors and corridors as edges can recompute every room’s route the moment a partition moves, and it notices when a route disappears. A tool that measures with a ruler will keep passing a plan whose corridor is blocked, because the ruler never checked. I’d rather carry the route and let someone who knows the adopted code decide what number it has to beat.