In combinatorial optimization, there are many problems that can be formulated as either Network Flow model or Mixed Integer Programming (MIP), e.g. supply chains, transportation, and graph-base problems. Some solvers make use of logical and/or graph-base syntax to efficiently solve network problems. And then the Network Simplex method is applied.
Also, As stated in Bazaraa, M.S., Jarvis, J.J. , and Sherali, H.D.; Linear programming and network flows, 4th Edition, Hoboken, New Jersey: Wiley & Sons, Inc., 2010; page 453:
We discuss appropriate data structures that facilitate the implementation of such a graph-theoretic procedure on the computer. The overall efficiency with which such a procedure operates enables one to solve problems 200-300 times faster than with a standard simplex approach that ignores any inherent special structures other than sparsity.
Practically speaking, from the aspect of time efficiency, are there any significant differences between modelling as a mixed integer programming and modeling as a network problem? And why (other than sparsity)?
Which optimization solvers are computationally fast at solving Network problems?