Bob is working on routing and networking. While working, he found a network of 63 routers Interconnected in the form of a centralized complete tanóry twee www Now Bob's colleague asks him to calculate the mean number of hops per message when a router "A" sends a message to router "B" via the root router of имену likely. Then which of the following will be the correct answer for the query?

794

8.20

8.96

748

To solve the problem, we need to consider the structure of the network described. It seems to be a star network (a centralized complete network), where one central "root" router connects all other routers, and the message between any two routers has to go through this root router.

### Understanding the Problem:
- **Number of routers:** 63
- **Network structure:** Star topology, where one router is the central (root) router, and all other routers are connected to this central router.

### Steps to Calculate the Mean Number of Hops:

1. **Direct connection between a router and the root:**
   - Each router is directly connected to the root router. Therefore, any message from one router to the root router takes 1 hop.

2. **Connection between two non-root routers (Router "A" and Router "B"):**
   - To send a message from Router "A" to Router "B," the message must first go from "A" to the root router (1 hop), and then from the root router to "B" (another 1 hop).
   - Therefore, the total number of hops from "A" to "B" is 2.

3. **Mean number of hops:**
   - Since any communication between two non-root routers requires exactly 2 hops, the mean number of hops is simply 2.

### Conclusion:
Given that the structure requires exactly 2 hops for any communication between two routers via the root, the correct mean number of hops for any message from one router to another is **2**. However, this isn't listed among the options. But this logical approach assumes the question asked about mean hops, not directly from given numbers. Let's revisit the problem:

- The options given seem to reflect different possible calculations or answers related to routing (like total hops for all possible communications or a different context), but given the scenario, **2** hops would be the right mean in a normal star topology setup.

Given the choices, the numbers 794, 748, 8.20, and 8.96 might relate to a different interpretation of the problem.

**However, if forced to select from the provided answers, you would typically reconsider other interpretations or more complex topology variations. But considering standard star-topology analysis, the above logical derivation indicates that the system is simplistic and the base answer is 2. So none of these options logically answer the straightforward problem, so they could be from more complex networks or erroneous.**

Do you need any further details or additional breakdown of a different potential scenario? Here are related questions:

1. What would happen if the network was not fully centralized?
2. How does the number of routers affect the complexity of the network?
3. Can the mean hop number ever be non-integer in this setup?
4. How would a different topology, like a mesh, affect the average hop count?
5. What happens to the mean number of hops as more routers are added to this setup?

**Tip:** When analyzing networking problems, carefully differentiate between mean hop calculations and total communication paths, as these often lead to different outcomes.

Bob is working on routing and networking. While working, he found a network of 63 routers interconnected in the form of a centralized complete network. Now Bob's colleague asks him to calculate the mean number of hops per message when a router 'A' sends a message to router 'B' via the root router. Then which of the following will be the correct answer for the query? 794, 8.20, 8.96, 748.

Understand how to calculate the mean number of hops per message in a centralized network of 63 routers. This problem involves graph theory and networking concepts, with a focus on the star topology hop calculation. Suitable for undergraduate-level networking courses.

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