Modify the example code so that edges are no longer directed but instead undirected (like pipes in which liquid flows); this means that the flow along an edge may proceed in one direction or the other, but not both. Verify that the algorithm still computes a valid maximum flow and that you are able to visualize the result.
Then, modify the edge capacities are no longer integers but positive values with decimal places. Verify again that the algorithm still computes a valid maximum flow and that the visualization remains reasonable.
Then, instead of assigning the edge capacities uniformly at random, use normally distributed non-negative capacities, with mean and standard deviation as adjustable parameters (crop all would-be negative values to be zero instead and remove those edges from the graph). Verify once more that the algorithm still computes a valid maximum flow and that you can still visualize it.
With the modified model from the basic stage, design and execute an experiment to determine the effect of the following factors on the average maximum flow over all possible source-target pairs in the undirected, weighted graph:
For each factor, determine whether or not an increase in it also produces an increase in the average maximum flow over all pairs.
When electricity flows in a circuit, the same basic rules apply as in the network flow of the example code: no flow may be stored at any vertex, and sum of the incoming flow must match the sum of the outgoing flow in any vertex except the source and the target. These laws of physics are called the Kirchhoff laws.
Read the Kirchhoff laws and about other phenomena in which a substance of some kind flows through an infrastructure of some kind. What are the attributes of the model? What kind of rules do the models obey?
Then, think back on the propagation models discussed in Week 10 when we spoke of epidemic spreading. In your own words, with your own illustrations, attempt to clarify the difference between flow and propagation as phenomena, indicating a handful of examples of each.
Finally, describe at least a couple of real-world situations that are a mixture of flow and propagation, situations in which a proper model of what is happening would have to combine aspects of the two.
When the flow is electricity, liquid, or gas, no explicit turn-taking, coordination, or synchronization is needed for the elements to pass. This is not the case in pedestrian or vehicular transit or when products progress on a production line in a factory or suitcases traverse the airport luggage logistics from the plane to the traveler.
Think about (or read about) how the model would need to be adjusted to work with a phenomenon that does involve turn-taking of sorts. Write down and illustrate your ideas, citing your sources (if any).