Ok, I thought they all started at level one.  Thanks.

This is why you view this from the wrong perspective.

It is an "adjacency" bonus, not the "level" of the building. If a building is not adjacent to anything that give it an adjacency bonus you don't get it. The number describe the number of adjacency bonuses the building gets. The level of the building is rather the upgrades you build.

At least that is how I see it and for me this is quite intuitive...

I thought that when you click once on an improvement, the number that shows up in the circle is the current level of the building.  If it isn't, where does it currently show the level of the building?  Also, buildings don't start at level one?  That seems counter-intuitive.

Buildings don't have levels, they are upgraded to new versions and each have it's own graphical representation. The number are simply the number of adjacency bonuses that building is affected by. You may call this the number of adjacency levels if you wish... zero means the building is not affected by any adjacency bonuses at all.

in a sense, the basic factory and similar T1 buildings really start at "level 5" (since they provide a 25% bonus which is the same as a +5 adjacency bonus). as you upgrade them, the better versions are essentially higher levels. a mega factory (third tier mfg building) has 40% bonus, which is essentially the same as "level 8". the manufacturing capital has a whopping 200% bonus, which sort of makes it a "level 40" building. 

that's how i view the building levels in relation to the adjacency. thinking of the buildings as "levels" instead of percentages is helpful if you have to make a decisions which building goes where and if it's better to stick a factory in the center of that 4 tile ring or rather a durantium refinery. stuff like that. 

the system is not that hard to understand once you realize that "1 level" and "5% bonus" are really the same thing.

Relatively old thread, but decided to respond because I was having trouble figuring out the level/adjacent thing too... Especially during a game where, researching Hives, and then giving the Hive the "Coordinated Hives" tech, I wasn't sure it was working right.  The Coordinated Hives tech reads "Increases the adjacency bonus of all improvements / Adjacency Level +1".  I assumed that this is improvements adjacent to the hive, not all improvements on the planet, since this is a specialization tech pertaining to hives.

The Yellow number on the improvement is the level.  It looks like regular improvements start at 0, get a level when you upgrade it, and adjacency bonuses improve that level as well.  For instance, I have a mega factory at level 7 (stated on the yellow number 7 when clicking the improvement, and in the tool tip when mousing over it, "Level 7", Manufacturing +35%.  The adjacency values (+1 for my mega factory given to others next to it) are what the clicked improvement gives to those around it.  To figure out the adjacency bonuses from other things to the factory, you have to do some addition.  So, my level 7 mega factory gets +3 from a durantium refinery, and 2 from the two factories next to it.  That's only 5, so we can surmise that basic factory is level 0, xeno factory is 1, and mega factory is 2.  So 5 adjacency levels plus 2 for being of the mega tier gives level 7.

Back to the hive specialization tech I selected, Coordinated Hives.  My assumption that the Adjacency Level +1 was given to any improvements next to the hive seems to be incorrect.  Unfortunate, because I planned to drop those suckers in the middle of some important non-manufacturing buildings to boost them all.  However, using the logic above with the mega factory, it seems the hive (getting adjacent bonuses only from manufacturing improvements) has an additional level now.  It's next to a Solar (+2), and two factories (+2), giving a lvl 6 Hive.  Therefore, hives must start at level 1 (not 0), and since I boosted my hives +1, it is level 6.

The hive level 6 gives a 30% boost to production, which is amazing, but the tech text should be updated to be more clear.  Or the game should be more clear in general - an adjacency level is a level, and a level (according to the hive specialization text) is an "adjacency bonus".  More than a bit confusing.

For someone not clear on Hive placement: get the level of your hive as high as possible with manufacturing improvements.  Each hive level gives +5% to production.

I think the text of the tech should be updated to say "Increases the level of all hives +1", because that's what it does.  It does not give +2 to adjacent improvements, still just +1.  Which is very nice, but not expected based on the tech's explanation.

Now if you'll excuse me, I have some realignment of planet economies to attend to.  *mumbles to self* hives in the middle of consulates and farms...