Nodes and edges model networks, circuits, schedules and routing.
A graph has nodes and edges, possibly directed or weighted. Concepts: paths, cycles, trees, connectivity, adjacency matrix. Applications: circuit analysis via nodal incidence, routing, scheduling with critical paths, and network flow.
A power grid is a weighted graph of buses and lines.
Graphs describe networks of connected parts, so they are used for circuits, communication routing, supply chains and scheduling.
Nodes and edges model networks, circuits, schedules and routing.
Graphs describe networks of connected parts, so they are used for circuits, communication routing, supply chains and scheduling.
A tree is a connected graph with no cycles. A general graph can contain loops and multiple paths between nodes.
It finds the shortest path from one node to all others when all edge weights are non-negative.
Typical applications include finding the shortest path for a delivery route, checking whether a circuit has a loop that causes a problem and scheduling tasks with dependencies in a manufacturing plan.
Study "Linear programming" first (topic 99 of 104 in Engineering Mathematics). It covers the groundwork this topic builds on.
Euler and Hamilton paths. Kirchhoff's laws are graph laws. Shortest-path and max-flow algorithms.
A power grid is a weighted graph of buses and lines.
The next topic is "Z-transform and difference equations", which builds directly on this one.
It is classed as Advanced in Engineering Mathematics (topic 100 of 104). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Engineering Mathematics.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.