How to Set Up a Network

In paminco, a network (or graph) essentially wraps the network elements Edges, Nodes, NetworkCost and DemandFunction as illustrated in image below:

Therefore, the network does not hold much data itself but rather passes requests to the subcompontent that holds the data. For example, if an algorithm sends a request to the network about the cost of a flow \(\mathbf{x}\): network.C(x), the network passes this request to its cost subcomponent and returns (a modified) value network.cost(x).sum(). The main network elements can be accessed via network.shared, network.nodes, network.edges, network.cost and network.demand.

We developed this architecture to achieve modularization and separate of concerns while allowing for complex cost and demand functions. Note that all network components need access to certain network attributes such as the number of vertices and links \(n\) and \(m\), as well as the the mappings of node labels to internal node indices that specify the behaviour of graph representations and demand vectors. Therefore all network elements have a reference to the Shared network object that in turn wraps nodes and edges.

For further details about how to set up a graph (directed or undirected) or specify demand and costs, see:

• How to set up directed and undirected graphs
  • 1 Setup
  • 2 Representations
  • 3 Edge bounds
  • 4 Labels to indices mapping
• How to specify the demand function for a network
  • 1. Why do we need it?
  • 2. Demand vectors and matrices
  • 3. Function types
• How to readin network data from XML
  • 1. Read edges and Nodes
  • 2. Read commodities
  • 3. Read edge cost
  • 4. Read the whole network
• How to plot a network
  • 1. Toy example
  • 2. SiouxFalls