Can we know the number of routers, bridges etc in the path of a message transmitted over a network? And How?

Answer 1

Running a tracert command at a dos prompt will show you how many 'hops' the connection makes...though in highly redundant networks, this could vary from time to time.

An example of the output is shown here, from my computer, to Yahoo....

1 1 ms 1 ms 1 ms 192.168.1.1
2 13 ms 13 ms * 68.208.230.3
3 13 ms 13 ms 13 ms 65.14.213.209
4 39 ms 39 ms 38 ms ixc01jax-pos-5-0-0.bellsouth.net [65.83.239.128]

5 37 ms 37 ms 37 ms ixc00jax-ge-0-0-0.bellsouth.net [205.152.187.64]

6 25 ms 25 ms 26 ms 65.83.239.74
7 25 ms 26 ms 25 ms 65.83.236.187
8 26 ms 26 ms 27 ms 65.83.238.40
9 37 ms 37 ms 37 ms 65.83.236.206
10 39 ms 54 ms 39 ms 65.83.237.228
11 38 ms 39 ms 39 ms ge-2-1-0-p140.msr1.re1.yahoo.com [216.115.108.17
]
12 39 ms 39 ms 39 ms ge-1-32.bas-a1.re3.yahoo.com [66.196.112.35]
13 39 ms 39 ms 38 ms f1.www.vip.re3.yahoo.com [69.147.114.210]

Answer 2

Actually u cant. U will pass thru a network cloud which hide all the network activities. The most u can see is ur ISP.