Routes and Networks
Routes and Networks questions deal with problems where paths, connections, or links between different points (cities, stations, people, or nodes) must be analyzed. These are usually represented as graphs or networks with nodes (points) and edges (connections). The task is to determine shortest routes, number of possible paths, or flow through the network.
Types of Routes and Network Problems
| Type | Description | Example |
|---|---|---|
| Shortest Path | Find the minimum distance or time between two points. | What is the shortest distance from City A to City D? |
| Multiple Routes | Count the number of different ways to travel between two points. | How many routes exist from A to C if A→B→C and A→D→C are options? |
| Network Flow | Analyze flow of goods/traffic through a network with capacity limits. | Max number of vehicles passing through roads per hour. |
| Travel Constraints | Path restrictions like “must pass through X” or “cannot use Y.” | Shortest route from A to D that must go through B. |
| Connectivity/Reachability | Determine if all points are connected or if disjoint paths exist. | Is the network connected if road B–C is blocked? |
How to Approach Routes and Networks Questions
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Draw the diagram: Convert the text into a network with labeled nodes and distances.
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Identify type of question: Shortest path, count of paths, or flow-based.
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Apply systematic methods:
- Shortest path → Dijkstra’s algorithm logic (step-by-step comparison).
- Number of paths → List systematically or use permutation logic.
- Flow problems → Apply bottleneck (minimum capacity along the path).
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Check constraints: Ensure mandatory or prohibited paths are respected.
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Cross-verify totals: Especially in counting paths to avoid duplication.
Conceptual Tips and Common Mistakes
- Don’t miss alternate paths: Sometimes shortest is not direct; detours may be shorter overall.
- Beware of double counting: When counting paths, avoid repeating the same route.
- Check for symmetry: In undirected networks, A→B is same as B→A unless stated otherwise.
- Capacity limits matter: In flow questions, the weakest (smallest) link controls throughput.
- Keep it visual: Tables and diagrams make these much easier.
Examples
Example 1 — Shortest Path
Distances: A–B = 5, B–C = 4, A–C = 12.
Shortest distance from A to C = min(12, 5+4) = 9.
Example 2 — Multiple Routes
Paths: A→B→C, A→D→C, A→E→C.
Total number of routes from A to C = 3.
Example 3 — Network Flow
If A→B has capacity 50, and B→C has capacity 40, max flow from A to C = 40 (bottleneck).
Example 4 — Travel with Constraint
If shortest A→C is 10 directly, but condition says “must pass through B” (A–B = 4, B–C = 5), then shortest constrained route = 4+5 = 9.