# Is there one word for both horizontal or vertical, but not diagonal, adjacency?

I'm trying to describe a grid and I want to say that the adjacent grid square is chosen if it's horizontally or vertically adjacent, but not diagonally adjacent, to the current grid square.

I was thinking maybe, laterally adjacent?

• Contiguous, if the two diagonal squares are not touching.
– KCH
Commented Apr 18, 2014 at 15:07
• Fails the "one word" criterion, but considering the question I think of the word perpendicular, as well as the phrase "cardinally adjacent" (that is, adjacent in a cardinal direction). Commented Apr 18, 2014 at 15:15
• @KCH contiguous does not seem to match: contiguous being in actual contact : touching along a boundary or at a point (from m-w.com) Commented Apr 18, 2014 at 15:55
• Not that I know of. Orthogonally adjacent is used. Commented Apr 18, 2014 at 16:06
• These questions kill me. How can two opposite things have one word to describe both together? Is that a word to describe UP and DOWN together?? Commented Oct 15, 2023 at 15:31

I've seen both "Orthogonally Adjacent" (Adjacent at right angles) and "Edge Adjacent" (Adjacent across edges rather than corners) used. They do mean slightly different things, but it's only relevant when dealing with something other than a regular rectangular grid.

Since measuring distance in this kind of topology is called "Manhattan distance" you might also try "Manhattan adjacent" although I've never seen that usage myself and it would probably require some explanation before using it.

• You must be a programmer too :) Thanks for this, I think I'll use edge adjacent. Commented Apr 18, 2014 at 21:19
• Do you have any references or sources for "Edge Adjacent"? I'm looking, but cannot find any. Commented Apr 18, 2014 at 22:44
• I found several when searching on Google for `"edge adjacent" "corner adjacent"` This PDF about Quadtree colouring makes the distinction in those terms arxiv.org/pdf/cs/9907030.pdf Commented Apr 19, 2014 at 19:44

Consider Orthogonal

Orthogonal - intersecting or lying at right angles

• But the two diagonals are also orthogonal to each other. Commented Apr 18, 2014 at 18:18
• @WanderingLogic I still think it makes sense, because the diagonals are not orthogonal to the grid, but you make a good point. Commented Apr 18, 2014 at 18:22
• This would answer the original title of the question, which only specified synonyms for "horizontal" and "vertical" -- they're all directions. There can be many cells that are orthogonal, but not necessarily neighboring/touching. Commented Apr 18, 2014 at 19:25

Abut: an area that is next to and has a common boundary with.

His land abuts mine

• But the answer should be an adjective :-) ... abutting Commented Apr 18, 2014 at 17:52

bor·der noun : a line separating one country or state from another; a boundary between places

(or bordering)

from m-w.com

Geospatially (not necessesarily mathematically) anything that was diagonal would share a point, which is commonly considered not a line. E.g. Utah borders Colorado and Arizona but not New Mexico.

• I sort of agree that bordering might be a good word to replace "adjacent" but you have to be careful with your last sentence. In geometry, the three undefined terms are point, line, and plane. Most math folks are comfortable with the common definitions but it's still considered taboo to say they have been defined and to compare those definitions. Commented Apr 18, 2014 at 15:04
• @jboneca Point taken; I've edited as appropriate. Commented Apr 18, 2014 at 15:52
• Your example is technically incorrect in so far as there is a point of Utah that touches a point of New Mexico, thus placing them at each other’s border. I suggest you choose a correct example.
– tchrist
Commented Apr 18, 2014 at 19:44
• @tchrist -- the example perfectly mirrors the OP's question. You may disagree that bordering is an appropriate word choice, but the example is not badly chosen. Commented Apr 18, 2014 at 20:23
• Border (horizontal and vertical) vs Edge (diagonal) seems like a nice pairing of terminology to me. Otherwise said as `border adjacent` vs `edge adjacent`. Commented Jan 12, 2022 at 3:16

If you want to say that the adjacent grid square is chosen if it's horizontally or vertically adjacent, but not diagonally adjacent to the current grid square, why not say that it's "nondiagonally adjacent?"

I think that the best term is rectilinearly adjacent. Compared to orthogonal, rectilinear has a stronger connotation of being axially aligned.

• I'd say "squarely adjacent" rather than any of rectilinearly, orthogonally, or nondiagonally adjacent Commented May 9, 2014 at 19:26

In this case, I like the term axial to describe a direction that is along the horizontal or vertical axis relative to the current position.

Axial - situated around, in the direction of, on, or along an axis.

• Axial as opposed to what? Is there another name for diagonal so they pair well? Commented Jan 12, 2022 at 3:16

Also consider

coterminous or conterminous: having the same or coincident boundaries

essentially, synonymous with bordering.

• I don't think this is the correct usage of "coterminous". Regions that border have part of a boundary in common, but I think "coterminous" means that the entire border is the same; that is, the two entities comprise the same region. Queens (the borough of New York City) is coterminous with Queens County (a county in New York); they're arguably not the same thing, but they have the same borders and they comprise the same region. Commented Apr 18, 2014 at 23:27
• @TannerSwett -- That is another meaning (one i only discovered today) of coterminous. The other meaning is to share part of a boundary. See onelook.com/?w=coterminous&ls=a Commented Apr 18, 2014 at 23:51

It's not one word, and I'm not sure how many people would follow it, but from cellular automata, you could refer to "squares that are in the von Neumann neighborhood of the current square".

The case you describe is called 4-connectivity, so the adjective you seek is 4-connected.

You can also say they are cardinally adjacent.

The cardinal directions are North, South, East and West, which conventionally map to up, down, right and left in 2D images. A Google search for the term "cardinally adjacent" has about 7,500 results at the time of writing, so this is a somewhat common term, although "orthogonally adjacent" has about 25,000, making it about three times as common.

I've been using the word "lateral" to describe this. It's defined as "Of , relating to, or situated at or on the side"

– Community Bot
Commented Apr 4, 2023 at 10:33

Grids in the form of algebraic matrices are ubiquitous in machine learning and statistical models, with many ways to describe the resulting relationships.

One drawback to their use is that the distances between the cells of a grid are typically fixed.

Network models are one approach to compensating for this fixity insofar as relative distances are approximated based on the function used...with the caveat that there are literally dozens of distance metrics, most orthogonal (not correlated) and others oblique (allows for correlation).

I can't find a specific example of terminology which answers your query but the field is rife with possibilities.

Check out this IBM white paper for an intro but note that network models are a large and burgeoning area of study.