Home

Welcome to the IdealFlowNetwork wiki!

What is Ideal Flow Network?

Ideal flow is defined as a steady state relative flow distribution in a strongly connected network where the flows are conserved. The ideal flow network (IFN) theory was first developed by Dr. Kardi Teknomo in 2014 in solving traffic congestion problem via ideal traffic assignment. He observed via random walk on small networks that the relative flow (which is the ratio of a link flow divided by the statistic of the network such as the min, max, total or average network flow) would always converge asymptotically to integers if and only if the network is strongly connected. Furthermore, such convergence values would always premagic to conserve the flow. Premagic matrix is a matrix where the vector sum of rows is exactly the same as the vector sum of columns.

The IFN has mathematical background based on Markov Chain and Maximum Entropy maximization. Based on the maximum entropy principle, we assume the maximum doubt when we have no data. The more data that we have, the result of the approximation would be more accurate. At the most parsimony level, the model can be run without any data aside from the network itself. The minimum data would be the adjacency matrix of the network.

The IFN is useful to approximate network utilization (the flow or the demand side of the network) via network structure (the supply side of the network). The IFN has been applied in the area of transportation, data science (machine learning), health science, ecology and industrial engineering.

Future Development

There are a lot of fun stuff to develop further and if you have any critics, comments or suggestions to improve, drop me a note. I would welcome your contribution by any means, your programming time, donation or scientific ideas and so on.

Do your part

We hope you find this IFN program useful for your study or work. Share your ideas in social media and compare it with your friends.