Drawing the line
How station order and track become a drawn line.
A straight line is easy to draw. Two ends, nothing in between that asks a question. In the graph this is a path of degree-2 vertices. Every station has one way in and one way out. The stroke can follow the order of the stops and be done.
Degree 3 is where drawing starts to fail. Three edges meet at a point. A branch leaves the trunk, or two arms join, and the vertex has to show that without looking like a scribble or a lie. A Y is the smallest honest shape. It is also the first shape that needs a rule.
Above that, the vertex stops being a Y. Four edges can be a crossing, or two corridors that share a name and never touch, or a diamond where every move is real. Five or six arms at one station cannot sit in one ring. Something has to peel away, stagger, or split into two nodes.
Degree is not enough. The same four edges sit differently in space than they do in the movement matrix. A drawing that only listens to permitted pairs will put the forbidden ones on the diameters and call that a cross. Compass order is one conversion pattern: same-side arms stay adjacent. When the matrix itself falls into two through-pairs that never meet, the vertex is not a junction at all — it is two ordinary lines that share a name. A degree-3 ordinary Y is the same fact with a terminus instead of a second through-pair. Both split before anything is drawn.
This is a diagnostic catalogue, not a map renderer.
Everything below is derived directly from TfL's own Route/Sequence data (via tfl-ts's LINE_STATION_SEQUENCES), independently of this site's existing line-topology and branch-schematic code. Adjacency, degree, and the movement matrix come from which stations sit back to back in a real ordered route or branch — a shared station does not by itself imply a through-service. TfL hub data is cross-referenced for identity only, not used to decide expansion or splitting. Station coordinates from the geography bundle seed arm bearings and distances only; they never create an edge.
Not solved here: label placement, octilinear layout, final line colours, geographic compaction, or peak/weekend service classification beyond what Route/Sequence names expose. The decomposition trees are a heuristic candidate to inspect, not a final answer — see each junction's evidence counts.
Conversion patterns
The point of this page is to name the weird vertices and the rule that turns each one into a drawable shape. Patterns land here as we can prove them. Order matters: split on the movement graph first. Compass order and same-direction spacing only apply to what is still one vertex after that.
Pipeline: split on movement components first
Adjacency, then the A–via–B matrix, then the connected components of that matrix. If there is more than one component, the station name is already several vertices. Each size-2 component is an ordinary through-run. Each size-1 component is a terminus. Two size-1 components at a degree-2 station are two termini. Bond the halves with an interchange and stop. A through-Y or a diamond is still one component — do not split those; they go on to compass order and lane spacing. Three isolated stubs with no through-pair stay one vertex until the source data proves otherwise.
Compass order, not chord order
Around a degree-4 vertex, never interleave opposite compass sides (N–S–N–S or W–E–W–E). Order the arms by geographic bearing so same-side neighbours stay adjacent. A chord diagram that only minimises crossings among permitted pairs does the opposite: it puts the through-runs on the short turns and the moves that never happen on the diameters. That plus-junction is a lie.
The production strip still drops a near-180° bend — the coloured arm already means “continues”. The diagnostic drawing keeps those through-moves, and draws the unsupported pairs dashed, so the matrix is visible on the figure. When two neighbours leave within a few degrees of each other they are a same-direction pair: two graph edges, one heading. The schematic has to invent a lane split; radial length on this page follows real distance so the further station sits further out.
Independent corridors become an H
A degree-4 station whose movement graph is two disjoint through-pairs is two degree-2 vertices that happen to share a name. Trains run Mornington Crescent–Euston–Warren Street, or Camden Town–Euston–King's Cross. They do not run from one pair into the other. Drawing that as one ring with four arms lets a forbidden pair sit on a geographic diameter and look like a straight through.
The conversion is the printed map's own device: stretch the name into two interchange dots and join them with a bar — an H, or an electric tower. Each upright is an ordinary through-run. The bar is a walk, not a track. The production strip already splits Euston this way; the diagnostic drawing does the same once the matrix says the corridors are independent.
Through-pair plus stub is the same split
Edgware Road on the Circle line is degree 3 with one through-pair (Baker Street–Paddington H&C) and one isolated stub (Paddington towards Bayswater). That stub is not a branch you can ride through — trains terminate. Drawing a Y pretends the third arm joins the trunk. The conversion is the H with one upright cut short: a through-station bonded to a terminus. Acton Main Line is the contrast — both Paddingtons through-run from Ealing Broadway, so the movement graph is one component and the station stays together.
Two edges and no through-run are two termini
Hainault is degree 2 with neighbours on both sides and no Grange Hill–via–Hainault–Fairlop run in Route/Sequence. The loop and the Leytonstone side both terminate here. Drawing one stroke through the name pretends they continue. The conversion is two terminus rings on a bar — the H with both uprights cut short. Heathrow Terminal 4 is the same pattern.
Cataloguing junctions…