Network Topologies · Study deck

Measuring Topologies with Graph Metrics

A network diagram with twelve nodes may contain one fragile bridge or several alternate routes.

Packet Pete is your guide for this deck.

analysis
Packet Pete, the module guide, in a scene from this chapter.
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After studying this chapter

Learning objectives

You will be able to:

  • Explain: Under the Hood explains degree, paths, cuts, scale, route overhead, and why several neat-looking shapes can hide the same failure domain.
  • Explain: The new edge adds installation and traffic cost, so the decision record should link that cost to the required resilience.
  • Explain: A star depends on its hub, and a tree on its parent branches; one shared role can isolate many leaves.
  • Explain: The shortest route from A to E is A-B-D-E, which has three edges.
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Major section

Start With the Story

If that relay fails, half the shelves disappear.

  • The network owner needs to see that weak point before release.
  • Under the Hood explains degree, paths, cuts, scale, route overhead, and why several neat-looking shapes can hide the same failure domain.
  • Topology analysis is the habit of proving that difference before release.
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Major section

Measure the Route Graph, Then Break It

Centrality can highlight a node that sits on many paths.

  • None of these values alone states whether the network meets its service target.
  • A node can have several neighbours yet remain inside one power or gateway failure domain.
  • Node B has degree 3, while A and E each have degree 1.

Key terms

B
B is therefore a critical articulation for A in this graph.
After B
After B is removed, A can still reach E by A-C-D-E.
Graph metrics expose node degree, shortest path, diameter, bridge risk, articulation risk, and weighted links
Graph metrics expose node degree, shortest path, diameter, bridge risk, articulation risk, and weighted links
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Major section

Measure the Route Graph, Then Break It (continued)

The shortest route from A to E is A-B-D-E, which has three edges.

  • B is therefore a critical articulation for A in this graph.
  • Adding edge A-C changes the failure result.
  • After B is removed, A can still reach E by A-C-D-E.
Topology decision record evidence map linking assumptions, graph metrics, failure tests, operations evidence, limits, and recheck triggers to one bounded topology decision.
Topology decision record evidence map linking assumptions, graph metrics, failure tests, operations evidence, limits, and recheck triggers to one bounded topology decision.
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Major section

Measure the Route Graph, Then Break It (continued)

The new edge adds installation and traffic cost, so the decision record should link that cost to the required resilience.

  • Calling the graph “more connected” is weaker than naming the protected route.
  • Metrics from intended drawings and discovered networks may differ.
  • A wireless link observed once should not automatically become a permanent symmetric edge.
Analysis follows a route from graph inventory through metrics and failure tests to a decision record
Analysis follows a route from graph inventory through metrics and failure tests to a decision record
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Major section

Practitioner: Build the Topology Analysis Record

Counting links alone cannot reveal whether the remaining paths are useful.

  • Router R1 degree = 3 illustrates: Node degree, while the highlighted route between sensors and the gateway, labelled: GW, illustrates one: Shortest path: Diameter is the longest shortest path, not simply the longest drawn edge.

Key terms

Diameter
Diameter is the longest shortest path, not simply the longest drawn edge.

Why it matters

A : Bridge link or relay can split the graph when it fails. : Weighted links attach retry rate, latency, quality, or capacity to edges that would otherwise look equal.

Graph metrics expose node degree, shortest path, diameter, bridge risk, articulation risk, and weighted links
Graph metrics expose node degree, shortest path, diameter, bridge risk, articulation risk, and weighted links
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Major section

Under the Hood: Failure Domains Decide Whether Metrics Matter

A star depends on its hub, and a tree on its parent branches; one shared role can isolate many leaves.

  • A ring becomes a line after a break.
  • A mesh needs an observed reroute before an alternate path can be treated as working.
Failure-domain comparison showing star hub dependency, tree branch risk, ring break behavior, partial mesh reroute proof, shared gateway boundary, and operations evidence to capture.
Failure-domain comparison showing star hub dependency, tree branch risk, ring break behavior, partial mesh reroute proof, shared gateway boundary, and operations evidence to capture.
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Deck summary

Key takeaways

If that relay fails, half the shelves disappear.

  • Centrality can highlight a node that sits on many paths.
  • The shortest route from A to E is A-B-D-E, which has three edges.
  • The new edge adds installation and traffic cost, so the decision record should link that cost to the required resilience.
  • Counting links alone cannot reveal whether the remaining paths are useful.
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Retrieval practice

Recall check 1 of 3

Packet Pete says: answer from memory, then check your reasoning.

Q1A topology graph shows one gateway with degree 40 and every cloud path depends on it. What should the analysis flag first?

ATraffic concentration and one gateway failure domain.
BA guaranteed full mesh because the graph contains many device nodes.
CNo gateway risk because high degree always improves path reliability.
DA reason to remove degree and path metrics from the topology record.
Show answer

Answer: A Topology analysis uses graph metrics and path dependency to find concentration, fragile failure domains, and the flows most likely to break under stress.

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Retrieval practice

Recall check 2 of 3

Packet Pete says: answer from memory, then check your reasoning.

Q2A 40-node warehouse sensor design compares a full mesh with a partial mesh where each node has about four neighbors. Which analysis belongs in the record before selection?

AChoose full mesh for every shelf sensor because one-hop paths will remove routing work from operations.
BChoose partial mesh for every aisle because fewer links will always improve reliability.
CIgnore graph metrics and compare only advertised radio range.
DCompare link growth and backup paths before choosing full or partial mesh.
Show answer

Answer: D A useful analysis record compares scaling burden with resilience evidence, then bounds the recommendation.

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Retrieval practice

Recall check 3 of 3

Packet Pete says: answer from memory, then check your reasoning.

Q3A building mesh appears connected in the design tool, but one wing repeatedly misses readings in field logs. What is the strongest next analysis step?

AAdd the protocol name to the diagram so everyone knows the network is a mesh.
BAssume all mesh nodes have equal relay roles and move directly to application debugging.
CReduce the sample rate permanently because fewer packets remove the network's path bottleneck.
DInspect weighted links, retries, neighbor tables, repairs, and shared failure domains.
Show answer

Answer: D Under the hood, topology health depends on weighted links, failure domains, route behavior, and operations evidence.

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Print reference

Answers

Answer key.

  1. A · Topology analysis uses graph metrics and path dependency to find concentration, fragile failure domains, and the flows most likely to break under stress.
  2. D · A useful analysis record compares scaling burden with resilience evidence, then bounds the recommendation.
  3. D · Under the hood, topology health depends on weighted links, failure domains, route behavior, and operations evidence.
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