Results of the Random Walk Algorithm on a Four-Connected Graph

We refer to the following connected, undirected graph as four-connected, because four is the minimum number of edges that if removed, disconnects the graph. More specifically, every node in this graph has a degree of four or more. The topology of this graph is likely to be the most common of the network topologies presented.

The following bar chart is loaded with information, so take your time reading it.

• Along the x-axis, we have all possible source-destination pairs. We can omit all permutations since order does not matter. For example, we don't need both A to B and B to A.
• Along the y-axis, is the frequency that a given edge (as denoted in the legend at the bottom) was traversed for a given source and destination.

The following two tables display the results obtained from 1000 executions of two source-destination pairs.

• The first table corresponds to 1000 executions where the communicating nodes are D and H. This table had the greatest number of unique routes.
• The second table corresponds to 1000 executions where the communicating nodes are G and M. This table had the least number of unique routes.

This information was collected for all source-destination pairs, but we did not display all of them for obvious reasons. If there are particular source-destination pairs that you would like to see the tables, please send mail to onion-info@itd.nrl.navy.mil and it will be included.

FREQUENCY	PATH
1	D A B A B I B I B L R N F C H E C H I Q I H
1	D A B A C A B C D G D J A J H
1	D A B A C B L R T P L B I B C F I H
1	D A B A C H J H K I H C F H I B A J H
1	D A B A D A D G E H I E H
1	D A B A D C B C D J H F C E H
1	D A B A E I B L B I B C H J H
1	D A B A J K H J K H C F N Q I K I B L B F I H E H
1	D A B A J H C B F E C F C A J H
1	D A B L O N F I E D J G K G E F N R S T P R P R S T S M O N F H E H C H
1	D A B L O T S T M T S R O P M P T P R L R Q N L M O N Q N Q O Q R L B I F H
1	D A B L P R O P O M O L R M P O L B A E G H I E A D C D J D E F H
1	D A B L Q I B F H
1	D A B L R N F H
1	D A B C A C E H
1	D A B C A C E I B I H G D E G E D G J H G J H
1	D A B C A J D J A J G E I K J H G K G J G H F E I H C F H
1	D A B C B F E I H E I K G K H J H
1	D A B C E A J K I K J G E D C B L O N F N F H K H
1	D A B C E C A E G H
1	D A B C F C F I H I B C F N R S R P O N O T S T S M R T O N L B F I F I F H
1	D A B C F H G H I F H K H
1	D A B C F I F E D E G H C F H J K I E C F H
1	D A B C H J G D E A C E G K G H K J D C A D G H
1	D A B F B C F H E F H
1	D A B F N Q O L Q N F H E D G E C H
1	D A B F C B L R P L B C B F C B L O T Q N F B C F C D J K J K H
1	D A B F C E D C E I H
1	D A B F E C H J G D G E H J G H G K H E C B F H E A B C H C A J D E I H F H
1	D A B F E F N F C A D G J D G H
1	D A B F H C F E C D A E A E F E H I F N Q I K G K G H I E D J K H
1	D A B F I Q I F N F H
1	D A B F I H C A B L N F B C D G J K H G K G K H J G H K H K G J G K H
1	D A B I B C F N F I K G H
1	D A B I K J K H
1	D A B I H
1	D A B I H C H C E A C D G H E H F N Q S Q S T R L R O Q N O N Q S R N F H
1	D A C A C E H C B I E C D C H
1	D A C A C F H G D C F N R T Q I K G H G D G D J H
1	D A C A D A D J K H F E C B I H I F H G J H C A E D E C F H I H J D E F E F H
1	D A C A D J G H J G E D C B L R O Q I F C D E H I E F E I K J H
1	D A C A J H K I B C B F I Q O Q S Q N L N O L B C H
1	D A C B L N O M T S T O P O R S M L O R Q I B L R Q I E G H
1	D A C B L N F E G J H
1	D A C B L P M L B A C F B L B I K H I F H I Q S M S Q S M T Q I H
1	D A C B C H C D G H G K J D G D G J D J H F E D C E I K H
1	D A C D A B A B L R T Q I F I E H
1	D A C D A C H E D J D J A J G H C H C H K G D G K H
1	D A C D A E H F E H J K H K J A C A B A B L R T S M L B F B C E G K I B C H
1	D A C D C D J H G D J H G H J G K H K G E C H J H E H C H K H
1	D A C D C F H C E H C D G H J D E D E C A E F B C E C H
1	D A C D E C E I H C H G J D E D J K G H I Q I K G E C A J G H
1	D A C D E I Q O N Q N F I H
1	D A C D G H G D A B F C H
1	D A C E C H J G K I H J A B C A D E C H
1	D A C E F H K I E A D J K J H C H
1	D A C E F H E I H J H
1	D A C E H I B F H
1	D A C F B C H K I F C F E H
1	D A C F B I Q N F H F N F I Q I E H E G H
1	D A C F N F E I E H
1	D A C F N F I B A C A C B L N O R L Q R S M P M O L M L N F I B F H
1	D A C F E G E A J A E C A J K J H C H F E I H C D A E A B C H
1	D A C F H K G H J A C D C B C H C B F H G K G K H G K H F H
1	D A C H K J D A C E I E I E H G E F C E H
1	D A C H K J G K I E D A B C B A B C H K G D G D J A D G H
1	D A C H C F N R L M R L M R N F H J G H C F H
1	D A C H E D A E A E C E D G H E F B F N R N O N R M L B C H I E F N F H
1	D A C H F C A B L Q L B I F E G J H C E D C D A D G E H J H K J D J H K G K H
1	D A C H I E H
1	D A C H J G D C E C A D E D C B L N O R N L R S R Q I F B I Q I H
1	D A C H J H C A E I E A B L Q I K J K G D G E D A D E A D A E I H
1	D A D A C B C A B F H
1	D A D A D E A D G D G J K H K I F H C F I H K H G D G H G E A E H
1	D A D A D J A D C D C B L N F C F C B I E H G H F H
1	D A D A E A B I H
1	D A D A E A J K H E F H K J K G E D E F I E H
1	D A D C B L R L B I H
1	D A D C B L R Q I H
1	D A D C B I Q L O L Q I B C H E C D A E C E C D G H J G K I B I H
1	D A D C D C D G J H I F N Q S Q R L B C D E G J A E F I F E G K G J G K J H
1	D A D C D G D E F H E C F I H G H E I H G D J K H
1	D A D C D G E A B C E G E D J G K J H G E I H
1	D A D C F C A C E I Q L N F E G J K H C H
1	D A D E A B I F H
1	D A D E F C F N Q N F I K G E A B I F H
1	D A D E G K G K G K J D G J G E F C B I Q T S M S M O L Q I E F E D A J H
1	D A D E G H
1	D A D E G J H
1	D A D E I H J K J G K J H F C B C E H
1	D A D G D C D G E G K G D C E C E H K I F H
1	D A D G D E A J A C B L Q T O R O T Q N F I H C E H G J G D A D G H G J H G H
1	D A D G D E F H
1	D A D G E I H F B C F N L P R Q T Q N F H
1	D A D G H J D C D E A C A C H
1	D A D G H J G J G H J D E A E D E H
1	D A D G J D E I H K J G J H
1	D A D G J D G H F H I B I K I H J D C H E D E F E I K I K H
1	D A D J K H C D A C H C B L R M P L O P L B I H
1	D A D J K H F B F H F C H K H I B L O N L B I H
1	D A D J K I B L B A B C F I H F N L M R O L Q O L B F H E C H
1	D A D J K I Q T S Q L O R S R L B F I B C H J G H
1	D A D J K J H F E D J H G D E I K I H K H G K I K G H
1	D A D J G H I B F I Q I H
1	D A D J G H J H F C A D C E G H I H
1	D A D J H C A C H
1	D A D J H E F I F E I F H
1	D A D J H E H F C A C D A D G J H F C F B I F B L B L B C A C B A C H
1	D A D J H I Q T S Q I H C F B L R L B C H E H I K H K H I H E A J A B C H
1	D A E A B F C D E G D A B I K H K I H
1	D A E A D A D C A J D J G E I Q L R N F C A B L N F C B F B F N L B F H
1	D A E A D E H C E D E F N R T Q N F I H F C F I B I E F I E I K J G K H
1	D A E A J K G J K J H K G E I H F C B A D G K I F B F B A B C B A C F E D E H
1	D A E C B I B L P M R M T S Q I F E F B A C D J A D J H
1	D A E C B I Q N L R L B I E H
1	D A E C D A J G D E A B A J D C H
1	D A E C D E G K G J A E F I H
1	D A E C E D J H
1	D A E C E H F H E A B L B I F N F I H
1	D A E C E H I F N F H K G J H J H K G J H
1	D A E C F C B I H K G H J G E D C B L B I B F C B I H K H F H
1	D A E C F E D A E C F I H K G J G H E C B C E F I Q O N F E D E H
1	D A E C F H
1	D A E D C B F B C H J K J H E F N L Q R S T M P O T R N O L B C H
1	D A E D C F H
1	D A E D C H K J H G J K H I Q N L R N L R S T O N F H E H
1	D A E F B F E F I K H C D J H E D C H K J K I E F E G J K H
1	D A E F B I K I B L P M T Q I K G K J K H G E G H G E I H
1	D A E F E D E D J D A C E H J K J K I Q T S T Q L B C D A C E D J D A J H E H
1	D A E F H J D C E I H K I Q L P O L N R Q N F N L P L B A E H C H
1	D A E F I H E C A D G E F H
1	D A E G K G K I H C F B L B C B I E D G E A C H J A E A B C H
1	D A E G K G H
1	D A E G K H C B C E H C A C H
1	D A E G K J G J K J A E H
1	D A E G D A B C A E A J H
1	D A E G D J H
1	D A E G E A B A D E C F I E D A D E A J H K H
1	D A E G E D C F H E H
1	D A E G E H
1	D A E G H I H C D C F C B C B I F H G D G J K J H C B C E A E G H
1	D A E G J D C B A J K J G E H C F H E A C B I K G D A E H
1	D A E G J H E C A C F N Q L R T R N Q I E D G H E G D E G H
1	D A E G J H E G H K G D A E A J K I E G D A C E H K J D A B A B A J H
1	D A E H K G J K I F N F I K H F C H C H G D G H C H C E I B C D E D G E H
1	D A E H C B A D E D J G H
1	D A E H E A B L R S T S R Q I H
1	D A E H I F I E I H
1	D A E H J H J D A J K G D C H J H G J H J A E F H F I K I E H
1	D A E I B C F E F E F I F H K G H
1	D A E I B F I B I H C H J K I Q R Q I B I B C H
1	D A E I B I F E D C B L Q I E H I K G D J G E F E F I H J H
1	D A E I K G H J D C F C B L R N L Q T M S R S T O L B F B F H
1	D A E I F B C H K G D C H C B L R M O T P R P L B C F H J K H G K I H
1	D A E I F N L R P M T S T P T P R N L Q I B I F B A D A J A D A J H
1	D A E I H K G K J G J H
1	D A E I H E I Q N F I H G E C H I H
1	D A E I H G J H C B I B C F N Q L M R Q S T O T R Q T Q I B A D J K G E H
1	D A J A C D C A D G J G D C D J K H I H G D A J H
1	D A J A J A J G J A D E H F N Q L O N F E G H C E C H K G E I K H K H
1	D A J A J K G J G H
1	D A J A J K H K H C A C B C B A C B C E I K I E C E H
1	D A J K H E F I F H
1	D A J K H I K I B C H I H I B C E A J A E D C F I E A D E F E D E A J D E F H
1	D A J K I B I F N F E I K H C H I F N Q I Q O P R N L R Q T O M R M O N F H
1	D A J K I F H G K J G K G K H C F E H G H K I E I H K H
1	D A J K I H G D E C B I Q R Q N O Q N F I B F C B A D E F E F N L R N F H K H
1	D A J K J H G D G E H I H I F E D G K J K J D E H G K H
1	D A J D C E D E H
1	D A J D E A C H F C F E H
1	D A J D E I K I B C A D E F H F I E C F I K H I Q O R L B F I K I K H
1	D A J D G H I H K H
1	D A J D G J A C E C A D E I H
1	D A J D J A B L M L O Q I B L R P M T Q L B C D C E F B A D G J D C H
1	D A J D J A C H
1	D A J D J K J D E G E G D J G D J K H F N Q I E A E D E G E C D A E H
1	D A J D J D E C B I F I F E F B L P L N F H G D G E H E G K G D A J G K H
1	D A J D J H
1	D A J G K G E F E F N L P L P O L P L N F H G J H
1	D A J G D J G H
1	D A J G E D C B L B C H
1	D A J G J G H C D C H I Q T Q I K G J D A E A J A B F I E I H G D J H K J K H
1	D A J G J H I Q S R L Q N F I B C B A E I H
1	D A J H K G K I F N F C D E C F H E F B F B L P R O T Q T Q I K I H
1	D A J H K J H I Q S R T R L Q N F H K J A B F I F E H
1	D A J H C B L O T Q O Q O T M S T Q N L N L B F B I F I F H F H
1	D A J H C B I K I B F C E D C B L P R Q I E G H G K I H
1	D A J H E A C H I B C F H
1	D A J H E A D J A E A C F H I F H K H F H C E A E G D C H
1	D A J H J A B C B F E G D C F E I E C B F H G D A C F E F H F H I K H
1	D A J H J A E H
1	D A J H J G J A B A E D C B L R N F H
1	D C A B L B A E I E I E H
1	D C A B L R N Q I E F E F H
1	D C A B C H E D E A C H K I Q T S Q S Q N O P L B F E I H
1	D C A C B C B L O R L B I B C H
1	D C A C B C F C H
1	D C A C F E C D J D E D C H C H I K J K I H C F B I B I F N F B I H
1	D C A C F I Q S T R M S M S Q R L B C H E C F E D J H
1	D C A C H K H
1	D C A C H C D J D J G K I E A B I F I F H J A C A J G H
1	D C A D C B F H
1	D C A D J D G K G E D C B L M O Q I H G J H G K I B C F H
1	D C A D J D G J G D G E G D C H
1	D C A D J H F C H
1	D C A E F N Q N O N R Q S Q I E G H I B I E H G H K H
1	D C A E G D A C B I E C B L P M S R P R M S R S Q I K J D J A C H
1	D C A E G D G D G K J D J H G J A E C H K I H
1	D C A E G H K I K H K G E I F I E D E C E D G E A C F H G K H
1	D C A E H F I K H I B I H I B F E F H F E F H J H
1	D C A J K G H G J D J D E G K J A B C H I B A J A E G H J D J H
1	D C A J K I E F H C H
1	D C A J D A B I H K J D G H
1	D C A J G E A B A E I E G J D J H K H
1	D C A J G E A C A D A E H F I F H
1	D C B A B L O P T Q N F B C A C B A J K H
1	D C B A C A C F C B I B F H E F H K G D C H
1	D C B A C A D E G E F N R N F H
1	D C B A C A J D E H I E D G E A B F H
1	D C B A C B I K J G D A E F E C E I B F C B C E C D G H K H
1	D C B A D G E F I F C F N R N Q T M S T Q N F I K G D G K J K G H
1	D C B A J A E D C D C B L O L P R L Q I H G K I F I H
1	D C B A J K I Q S Q I E I E H K H
1	D C B A J K J G E A E A D E G E H
1	D C B L M T P R S M T Q L B C E I E C H K H J D A B L Q I H J K I H
1	D C B L N F C D E F C H
1	D C B L O M T Q I H G J H
1	D C B L P T O R N Q N F I H E A D G J G K H
1	D C B L Q R M O Q N F I H G J H G K G E I H J G H E C F H
1	D C B C B A C E G J K H E I E D G K H J K G E I F E F E D C H
1	D C B C E C B F E D G E C E F I H G J A B L B A E F I E D G E D G K H
1	D C B C F N L R N O L R Q L M R N F I H K J H I B F H
1	D C B C H K H E H K I F E A D C A J H E C E C B L P L M S Q I H
1	D C B F B L M O T P L R L B F H G H
1	D C B F B F N F B A J H
1	D C B F C A E A J D G J G K J G J A C H K H I H
1	D C B F I F N L N F C B F H
1	D C B I Q L B L R Q R N Q L B A E H J D E H I H
1	D C B I E C H
1	D C B I F N F E F N R S R L O L O R L B I F H J D E A J G K I F C H K G H
1	D C B I F C B C H
1	D C D A C B C H
1	D C D A C F H
1	D C D A C H F N Q N F H J K H
1	D C D A D G J A C H E D G K I B F C B C H
1	D C D A E G E H
1	D C D C A B F N R O Q N O N Q L B I H G E I B I E H I Q L B C D E I K G J G H
1	D C D C A B F H I E A D A B I H K H
1	D C D C E C E D C D E G H I F I Q T S Q L Q I Q I F H I H
1	D C D C H E F H J H K H J H
1	D C D C H I H G K J H I F N F H F B I K I E H
1	D C D E A C A J D G J G H F I Q T Q L N Q N Q R M S T P R L N F C F N F H
1	D C D E D C D J H I K J H J A C A J H G D G H
1	D C D E H F N L O N L R P M L O M R Q N F H I H J A J H
1	D C D E I E I B L B F N Q O T S M L N R M S M R S R S Q I H
1	D C D E I H J K I H I Q L Q I F I E G K J D C F B A B C H F B A C H E F H
1	D C D G D A C F E I Q L B C D C D A C E F E D C H
1	D C D G E F N R O P L B A B A E H J H
1	D C D G J G D C F E A J D E D A C H E D E C E D G J K H C A B F B F H G H K H
1	D C D J A B L M O R P L N F E F B L Q N F I E D C H K G K H
1	D C D J K J A B I H F B C H I Q N F I E I B I B A B I B F B F E H
1	D C D J D C H
1	D C D J G K G H G D G H C H E A J A E D C B F C D A C A E H K J K J H
1	D C D J H
1	D C E A B A J A C B L B A C H G E G J A C H
1	D C E A C B I H G E A B F C E F N L Q I H G J G D A B F B A D E H J H
1	D C E A C D C B L P L N F H G H
1	D C E A C H K H J D E I K J G D E H I B A D G K J A J G D C D C D J A C H G H
1	D C E A D A B A E F B C F I B I Q N L R L B A C E D E C H C B A B F H
1	D C E A J A E G D C A D G J K H I B C E I K I K I F I F H
1	D C E A J D A E G K H J D E I K I K I H K H
1	D C E C E A D C D J G E I H G D G D G J H F E C D E H G J A E C H
1	D C E C F B I B I H E I H
1	D C E C H
1	D C E C H K H G K G E I E D C E F E A C F H
1	D C E C H E H
1	D C E D C F N R Q L O L Q L Q I K I H
1	D C E D C F H I K H G D J G E D G J A B F B F E H C A C H J H
1	D C E D E D G E C A J G E D C B L O L Q N F H
1	D C E D E G K H F H
1	D C E D E G J H
1	D C E D E H
1	D C E D G K H F E A B L N R Q N F C B I H J K I E A J H
1	D C E D J K G J K H C A D G D E F H E A C F E D J H
1	D C E D J H C D J A C F H F I K H J H
1	D C E F B F E C D J A D C F B L O T P L B C F E I E D E A J H
1	D C E F N O N L Q L B C D C D A C F B I E D C E H
1	D C E F N Q T O P L B F H C H
1	D C E F I K H
1	D C E F I H I Q S T P O P M O Q O L R S Q O P T P O M L B F C H C A J H
1	D C E G K H F C D A E I K H F H
1	D C E G K H I K G H F I K G J H
1	D C E G K J D A C E A D J H K J G D J D J A C B A J G E H J D J H
1	D C E G D G H I B A D J K H G D C D C H I Q T M L B F I B A D G E G H
1	D C E G D J A B L Q R P L Q L B C A B L N O M S Q L B A B F B A J D E F I F H
1	D C E G D J K I B L M P T O M R L B C F N F H
1	D C E G H F C B I E F I K J K I Q I F C D A J G K G K G J H G H
1	D C E G J K H F I F I F N L N O P M L O T P T R N F I B C B C E F H
1	D C E G J G H K H J K G E D E F I B F I F N F C A E F E F H F H
1	D C E H E I B I F I H K G D A E D C D G E H K J H
1	D C E H I H F N O M P L Q N F H E D G J D A C H
1	D C E I B F N Q T Q O R Q L Q T P L N F E H
1	D C E I Q O N F N L P M O T R O L Q N F H F I H I H K I H
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1	D C E I Q I H I H G E C B I H G J D J H K J G K H C D G H
1	D C E I H G H G K G J K H F I H J K I K I H C F C E C H C E D J H
1	D C F B A E C B I H J H J A D A C D C F C H C H I H E A J G J H K G K I E H
1	D C F B A E D G E F E I B L P M R O R P T M P O P T Q I H
1	D C F B L B C B C F I K H C H
1	D C F B L P L N L M R P R N F C B F H I K H E F N F H
1	D C F B C H C F N L Q T S R L B I F H
1	D C F B F C A D C B A D E F H I H F N F H J G K I E D J H C F C F H J G H I H
1	D C F B F H K I F H C F C B F N F N F I F I B F B A J G J G E G D C H
1	D C F B F I B L N O P R L B C E A E C D G D G J D G E D A C H
1	D C F B I F E C H K H K H G D C A E G K H
1	D C F B I H C A D G H I B F E H J D J H
1	D C F N L B F B C A E H J K I H G J H
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1	D C F N O Q L P R S T Q R T R T Q I E I F C A C A D C B A J G H
1	D C F N O Q T S Q O Q R L R T Q N F E C F B I F E D J G J A J G J K H F H
1	D C F C A C D C H I H K G D A E I F B C H C D A D G J H E G D E H
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1	D C F C A E G D E A J A C E F H J D J K J G K H J G K H
1	D C F C B F B L O L B I H G K G D A C A E F E C A J K G H
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1	D C F E D C H J H C H G D G K G K G H J H F H
1	D C F E F H K H G E C D G J D C A C A E C F I H E D J G J G H
1	D C F E H E A E D C A C A J D J G E F E I B I F E H
1	D C F E I B A D C H C D C B C E A J H J G E F H
1	D C F E I H G K H G H C H K I K I H G D C E D C B C A D J K I K J D G H
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1	D C F I Q N L Q R N Q T S Q N F B A B A D A B I K G H
1	D C F I Q O Q O L B F C F I E A J G D E G H E F B A D E H
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