How to use trained neural network in different platform/technology?
Technically you don't need a framework at all. A conventional fully connected neural network is simple enough that you can implement it in straight C++. It's about 100 lines of code for the matrix multiplication and a dozen or so for the non-linear activation function. 
The biggest part is figuring out how to parse a serialized Tensorflow model, especially given that there are quite a few ways to do so. You probably will want to freeze your TensorFlow model; this inserts the weights from the latest training into the model.
Given I trained a simple neural network using Tensorflow and Python on my laptop and I want to use this model on my phone in C++ app.
Is there any compatibility format I can use? What is the minimal framework to run neural networks (not to train)?
UDP. I'm also interested in Tensorflow to NOT-Tensorflow compatibility. Do I need to build it up from scratch or there're any best practices?