I installed loki on both, VMware Player and VirtualBox; it did not install software center on either. I tried to install it (1) from the appcenter - and like described in a previous note, it just hung showing 'starting'. (2) I tried a manual install with apt-get install software-center - it showed serveral failures with the basic message: No module named 'softwarecenter.distro."elementary"'. It did create the software center icon... but it can't be executed. Removing software center with apt-get purge software-center also results in several error messages, with a final pop-up to report the problem. As the documentation describes software center as a basic 'feature' of elementary this really should work straight out of the box!
Here is something that I found on:
"Now, there are two ways to install the .deb packages: command line way and GUI way.
If you go by command line, there are numerous ways to install the .deb packages but I’ll go with the simplest one. Open a terminal and use the following command:
sudo apt install
Alternatively, you can use a dedicated GUI application gDebi. gDebi is a lightweight and yet powerful application for installing .deb packages. It is particularly useful in handling dependencies. This is why I have often advised to make gDebi the default application to install programs.
You can install gDebi from the AppCenter. Just search for it. You can also install it via the command line. Just use the command below:
sudo apt install gdebi
Once you have installed gDebi, right click on the .deb package and choose to open with gDebi. That’s it."
There is also the soluntion found by this user.
By doing this you should be able to install ubuntu software-center as they have explained.
Hope this helps.