Designing a Communication Network for a Smart Campus

In this scenario, you are working for a university that is implementing a smart campus infrastructure to support real-time communication between devices, sensors, and control systems across multiple buildings. Your IT team must design a network that ensures reliable connectivity, efficient routing, and scalable architecture.

Your team models the campus network as a graph. Vertices represent devices, routers, and control hubs. Edges represent communication links between devices.

They use different types of graphs to analyze and optimize the system:

1. Complete Graphs: In the central control room, all monitoring devices must communicate directly with each other to ensure redundancy and fault tolerance. This is modelled as a complete graph, where every device is connected to every other device.
2. Connected Graphs: Across the campus, the network must be connected so that any device can reach any other device, either directly or through intermediate nodes. Your team verifies that the graph representing the entire campus is connected, ensuring no isolated components.
3. Directed Graphs: For data flow between sensors and control systems, your team uses directed graphs. For example, temperature sensors send data to Heating, Ventilation, and Air Conditioning (HVAC) controllers (sensor [latex]\rightarrow[/latex] controller), but not vice versa. Incoming and outgoing degree analysis help identify bottlenecks and optimize routing paths.

Task 1

Model the control room network as a complete graph with 6 devices. How many direct communication links are required?

Task 2

Verify that the campus-wide network is connected. What strategies can be used to restore connectivity if a router fails?

Task 3

Represent the sensor-to-controller data flow as a directed graph. Identify nodes with high incoming degree and discuss their role in the system.

Task 4

Determine whether the directed graph of data flow contains cycles. What are the implications of cycles in control systems?

Task 5

Propose a graph-based strategy to scale the network as new buildings and devices are added.