Welcome to the forum, csimon.
I took the liberty of turning your PDF drawing into an actual image and indicating more plainly what I think your objective and concern is. Click the image to see it full-size:
It appears your plan is to start in what I believe is a dining room. The long orange lines and arrows indicate the direction of the grain. You may be unaware of the availability of "spline" material for most hardwood. This is a manufactured tongue that can be slipped in the groove side of any board to reverse direction (some pros refer to the spline as a "slip-tongue"). This makes your problem go away.
However, your starting wall will create an even bigger problem. Starting in a small room all the way to one side of the house will pretty much assure you that by the time you reach the other, your layout will not be square with the walls.
Start in the middle and work in both directions. Choose the longest and straightest run you can get, which appears to be from the top of bedroom 1, through the hallway and to the bottom of bedroom 4. Start with as many rows as it takes to do most of the width of the 2 doorways you're going through. Then spline the groove side and continue the installation to completion. Use a spline whenever you need to change directions. See my altered diagram to illustrate (click to enlarge):
This may also cause a problem in the expansion and contraction of such large expanses of material. That will depend on the material and its properties. You may find it necessary to put a transition piece in the doorways that allows you to separate the areas so its effects of movement will not cause problems. The only reason I include this caution is because you didn't provide any measurements, nor did you give us the product specifics - manufacturer, species, quality, etc. In many cases, you will not have to worry about these expansion/contraction issues in the average home.
Some of our other pros will have more information and may correct any mistakes I may have made. Stick around and we'll try to help where we can. Thanks for being here.
Jim
PS: sorry if I got any room names wrong. it shouldn't matter in the grand scheme of things anyway.