Results of the Random Walk Algorithm on a Clique

The following graph is a clique. The figure below is a 6 node clique to illustrate the topology of a clique. Although not shown here, our experimentation utilized a 20 node clique.

The two following bar charts are loaded with information, so take your time reading them.

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 significance of this graph is that even if a given source and destination frequently (or even always) traverse an edge (and thus two nodes), this should be considered in light of how frequently all other communicating endpoints utilize the edge. For example, suppose source X and destination Y use the edge(U,V) 100% of the time. If many other source and destination pairs use this same edge with equal (or close to) frequencies, then our concern is diminished. However, if other source and destination pairs rarely use the edge, then the fact that X and Y continuously utilize the edge might be problematic. Recall, this algorithm was executed 1000 times.

Since a 20 node clique has many edges (190), we needed to separate the following data into two bar charts.

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

Both tables are sorted in ascending order according to the frequency number.

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.

FREQUHNCY PATH

1 H A B P B A I L J A J H D H D M G R N G B I B A K T S N S E K B I D G N

1 H A B Q L D P L R N Q B A H D N E T J A C N C S B H N I B N C N

1 H A B T N

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

1 H A L T D M Q F T S A C J L H R D F D R D H L N

1 H A M A M S A D J L C K O R Q N

1 H A M R E N J B H S B H S R T E J Q T K O Q C A M D F D S T M N M S N

1 H A M S B N K S C O T H Q N R B E J H P F S N

1 H A M I H A J B D F R J P N K S B L A S E G C D P C D K B D J A G A J C L N

1 H A N A N H O K H A D N M G E A M J I D A N

1 H A N B Q F O N

1 H A N R N I Q G L T F Q K J P C P H J D G N

1 H A N E M H B Q F B F O K E B O J A E O F N B G H C O K T R N

1 H A N F R D A N E N

1 H A N H O Q N L C M B H S B S B G K N T J N

1 H A O N B P H C Q S D I D T S C F P E C Q F R S K P D F M C H N R P M T R P N

1 H A O D P Q F K I F J S A P L C K N O E F G N H C O Q N P T S J N

1 H A O D C A J S R B F O H Q L B C J G O N

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

1 H A P H N

1 H A Q A M O R H T N R L A J E A Q S A C G R K N

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

1 H A R O N C Q B C O L F P A O G N

1 H A R I G F M F E L F R O E Q E J M F E N O G J K N

1 H A R I J C M S L I J E M D A M K B E B M D I R I Q N

1 H A S G T N J N Q L J H L K N T I L J L P B K N

1 H A S I O L N B I R O G Q A K T H O N

1 H A S I S H O L D T O N B I L A I M K N O I S H I A H S F J N

1 H A T N D B H N Q J D C E O E D R P Q A P R B R J P M B E N

1 H A T S G O B R H D N B S N G S A D L E K P I G D J L R L F S K J R N

1 H A C L M P S Q C S T S K A G H R Q M N B Q M O N

1 H A C O G A O E J E C L J H A I J N

1 H A C Q L N

1 H A D A J P A D B K D M N O H N

1 H A D N K D H Q N

1 H A D T K L A G S B O C Q N L O E O I B G M J M T G S N

1 H A D T H T R J Q S E Q G F P S N

1 H A D E R K I T D M T P G A Q M E B S C S B N

1 H A D H B I N L J M K A G L M O N B G K C L N

1 H A D I G S P R P L G S A C N

1 H A E O N

1 H A E O R I B L N I N

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

1 H A G D J N

1 H A G J P L O N H B I P A I N

1 H A H A C I B C F S T N E O M S J F H L K Q O N

1 H A H P M J K D Q H D Q F S D R P G L G C D B A N

1 H A H E G B S J T S D L P E H A R P K N

1 H A I L R L F P R I G P I L N

1 H A I Q M T A G T A B J L M A Q J P L Q I R F S L R P N

1 H A J C N I H K H T A H S B E M D E P K O K D N C O B C L C D P D S N

1 H B A M R Q H G M B C A N C A J O S R H J G B I H D F P L N

1 H B A M H P D C H P Q T I A I S H G F E O M C A T F M J O T M C T P H N

1 H B A E P A H D P F A F D T J N K L I T S A T A S E O T K N Q S I A P T H N

1 H B A F E F B O E P O Q L J A M L I L M L R T N

1 H B A I B I D K M D C S F S I B P H J P S N

1 H B A I P N K R A H R I M S T E O L I B H R N

1 H B K M S E P A J L K F P O I C H A T G S G M C T J A N

1 H B L A B P G A Q L K P B L K H N T B M N

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

1 H B L J I F P J O L P S K N K M K B K M O B F T A E A H M O N

1 H B M B L I S P I Q T N S A H B I H L F J M J I K R N A N

1 H B M O E N M N

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

1 H B N

1 H B N O L J A C L P N D H N P F D E D F S N E A G F S L B Q H I J P C O N

1 H B N O Q P R O J O E L R F M S R N

1 H B N R E J D L H G C Q A L I N

1 H B O L Q O D R S B T K I B N Q J E G N

1 H B O M R S O I O N O D G A G M K F N M N

1 H B O N G A R K O R A D P M E P E T K L N

1 H B O F C K N H J A G P K H Q N

1 H B O G B G F G C E B P H A L R T N R Q G P H A P C D F H J M E M C O L N

1 H B P L O G A N

1 H B P F S A J O E F D M J O N

1 H B P H F R J T K R T F R E D O H Q J N Q C L E I Q N

1 H B Q L D A S O I G A P C Q K N

1 H B Q O R C R C L O J E M D A N S J C A Q N H I L Q G J B R N

1 H B R B F J Q F N

1 H B R K G J D M P S G B J P R O J S A E K A O N R G O D H A E M E J K L N Q N

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

1 H B T M N C M Q I S C D P F R I K N O A H O N K D E N

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

1 H B T C P G H S L J M H P T D S P C P F A R P B C H N

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

1 H B C M G Q F Q P B T F S C A M T M C T S F M J O G E L N

1 H B C O F L I T M E J B T N

1 H B C Q H M D T I P T I F D F I N I T H A L N

1 H B C S H I K S F M B O N

1 H B C D R P I P N

1 H B D A G D T B I L H G N M N R D N G E N Q K M T H N

1 H B D O F D B C E T N

1 H B D E D N B R M F S Q F S R C F M J I S P C P E N

1 H B D H G P F Q S D C F T E M E N

1 H B E A S L C F K J M Q A G M R D I R N

1 H B E C L N T E Q B A B I D T Q N

1 H B E G K R N L P O B O C M T S A J A B H C S P F S L E G L B R N

1 H B F N

1 H B F P M A E M O D P H J H J Q M J O A P Q B E A E R E C K N

1 H B H T J P A Q R I G Q E F H J E F A M S M H N

1 H B H D G B H P R O M N

1 H B H G S H B S P D L P I T S D M L P G Q R O G S K Q F K P Q L P G N

1 H B I M O I M I L N S B N

1 H B I Q H D I T P O K S N B P S A B A F L H B D G I K S M N

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

1 H B I G E B F D I F G T J P O K F O N

1 H B I G F G C D B R K N A N L S N

1 H B J P N J N

1 H K B K L Q K N P M F R I B Q E A H N

1 H K B K O T R G O H F G O Q O K I N P Q A E A G C Q H A N

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

1 H K B T G D F K D N P Q S Q I L A P E F N P D L G S B C E H O N

1 H K L C K F K H I D N

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

1 H K N C Q O M C R O E F E J A O P A R O M C H R N

1 H K O B S T B J A L M E Q G S F N H T C K O I H N

1 H K O K R M I T M L N

1 H K O N C Q F G L O E S I B M C D B Q B L O D N

1 H K P B N F G I L I K D B D F Q K S R Q P I O N

1 H K P N S G T E J E K R S L C T S Q L O F T J K L Q P N S G J D N

1 H K P C D N B E F C E M B D G F J P G P H I D H T F G Q G K N

1 H K P D L E N D A N

1 H K Q A M O K C I M O S Q R I A I E N

1 H K Q L E N

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

1 H K R L B I B R I F J A L F I J I M R N K O K F A G B N A B F C Q M I N

1 H K R P A E O L F C E J F E O J A D M R N L E B N

1 H K R Q L E J C I H N

1 H K S B I F N

1 H K S Q G E B I R T A E F K M O Q I J B I N A N

1 H K S Q I O N H I N D I T N M Q A G D C B D C D A N

1 H K S T G I D C I G N S L D E P G R J C H T L E J B N

1 H K T P G F N M E T H J A P O A Q M N P A T D T P C F P C Q I Q G C M B Q E N

1 H K T Q R O G M D O R K T J M Q R I N S E P O G N

1 H K T Q E B I S N M Q I Q L H P M G I E N

1 H K T R K T N

1 H K T C F T K S T L P G D N E H R Q H O B E H T P M N

1 H K C L H I N

1 H K C H T M N H G M D B M S O G R G M F S M O P B O R J I R N

1 H K D A O H D M G H J Q D N

1 H K D C E Q L E T O S J N

1 H K E K D S K N B J N H K C B Q S L D J D H K F A R K T I H G J F N

1 H K E L P N M Q R J N

1 H K E C I F G N O Q I Q H R N M S D O P I Q K S T P N

1 H K E D C H L M C G C K B T S L M K T N O D N

1 H K F I Q F E M S H N E L Q C A B A D F N

1 H K G A Q P N O E F G B R E K E K G N

1 H K G L I O N C H R J Q N T H L D A S R J P T E A C L A J D H N

1 H K H M P N M Q A F T K J P M P A P F Q M N

1 H K H O N R M O S N

1 H K H C S F K A Q I F O G A H T J M L Q N

1 H K H F M L F S Q H S N P I S C M S R P M N

1 H K I N C M K R Q L E J F N I N

1 H K J H N M Q A G H A N

1 H L A K C A J E M L H T Q N

1 H L A N I B S J H N

1 H L A Q J L F H R K R L J S N F S M N O H L Q F S P Q K P D C M I R N

1 H L A G E P T R D K F E C L G H E C N

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

1 H L B N K Q B I R B M N

1 H L B Q C D M N E L Q C A J S Q R C O Q R N

1 H L B Q G L D G K J K A P A L A J O E F B T D Q N F R O B P K O N

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

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

1 H L K H K C N

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

1 H L M S F G N A Q A T N J M H N

1 H L M D R N G Q P Q I M I C F Q G O G H R A O G J N

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

1 H L N

1 H L N L E J O S E N B H G P B D N A O D H N B R Q B R L A L M B D P N

1 H L N S H C J M N

1 H L N C L D A S D I J T N K A J N

1 H L O Q S G D O E K I D B D B M J N L Q R K B I A J P J P O P N

1 H L P K E R D H P B N

1 H L P L H N S O P I B S P L P T A O J L N G B J K I D H D E N T N

1 H L P O C M J O K B L O T M N

1 H L P O F K A N

1 H L R A C J I F A R E O C O Q O L J M T S K A B Q B A K B O Q F T M N

1 H L R A J Q M D H O C I D O R L J F P N

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

1 H L S O A S K G K T C D M K S J G E N M S A K G M A E H T R N

1 H L S T J M L I H M J R B G N

1 H L T O Q G L B N

1 H L T J L A D C K P B D N

1 H L C B G J A Q M J O E L H T N

1 H L C N P J B S T B D L K M S O K I N C I S T H K N B Q R E D R H D N

1 H L C S F A R N H F E K D H B S L A B E F R N

1 H L D R D A L R J K R O G Q I D T F P J C N

1 H L D I G O H R D I J F N M Q B J Q C D H M N

1 H L E M F G B I Q M J L K G Q G R B O N E L Q C M K J Q S C N F H L N

1 H L F E Q T J I N P F B T L D Q S P F C E A S J D Q J D Q A O J N

1 H L F E I T M D L C J P N O E F G Q S J M D A N

1 H L F J G O N D Q I O H C D M E G B D K H O G H N A N

1 H L G P G P H N O F D B D O S A J O N R T F I H G H A K G M N

1 H L G Q C A G L N

1 H L G R Q H E M J T G F R L H M G N O I N

1 H L G C E J O D N A S J Q G L N L I B P R N R T I R D B N

1 H L G E C G Q O T E N T P A R K R K E A B R K B C E B H A O C T M H N

1 H L H L E C L T D J O F J E N D P F K G J T B K H R D N

1 H L H P R L R M L B J L N I C K S T S J R H C N A R N B N

1 H L H R P J P E H J Q H Q C R P N

1 H L I L K P N H G N S R K O D R G J M N

1 H L I D O S M N E H A L F I M Q L S M N P M E G H B O D N

1 H L I G S G D P I N P B H K E N J P Q N

1 H M A F B Q S E O M J R K L E I N

1 H M B Q C J Q K M R T B F A C J G P L F R M A N

1 H M B G F M L Q M H N

1 H M K A D L H S C A N C P N

1 H M K S C H M J K N J H G O F R N T Q L F L A P N

1 H M K J E J E M L N A D Q L A C O F Q R N

1 H M N T H I T F P E S N

1 H M N E L Q C S L N

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

1 H M O K H O P I C K P C M C L P T J N

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

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

1 H M O E N

1 H M R A C N

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

1 H M R K E P G K S B E N S T N

1 H M R S D I N

1 H M S A J P G J O K H O B P I H Q S F L M F Q P N

1 H M S K P T R K S Q M A T A T G S G S P J N

1 H M S D N E S Q F C S Q I S L O F P N D M D N K N

1 H M S F M B M A E T I S G C L Q B K H B Q N S N L T N F H D T L E B E G N

1 H M S F N

1 H M T K R I R N

1 H M C S L D G L Q L Q N B L H I B M R M C F A R Q R I D G E M N

1 H M C D G A T R B M O J A G A H L M J N J C M J M N S A C N D I J E F B F N

1 H M D A I Q K N R I S O T E G A O S H O N

1 H M D P N O E F G C G S G J O T N

1 H M E B O P G Q T N L O J E D M T K S I A P N

1 H M E K T K G K E H M L I K S B J S N

1 H M E N F R N

1 H M E T E Q J C A P S A T B A M O C J P L N L N

1 H M E F M O P G T R O G I T N

1 H M F S P C O F O F A T H N L O R E G E N D S E H E N

1 H M G K Q B J G D Q S D Q R C L T F G H M I S B I H L A K A M T B D N

1 H M G T J N I N R Q L E B P L K M I N S E N

1 H M G F M K A B F G N A D O F E R B F Q N

1 H M H K D O J R S F O E H N O E N O M I L R F D E T K R J S G H N

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

1 H M H E D K C L D T N

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

1 H M I E J H D C B J M P M O D I K A D N

1 H M I J R N D O F R K N H A T Q A H N

1 H M J Q G K C N Q N H P N I B K I D O H M S Q E S I K N

1 H M J Q G F B H E P F N

1 H M J E M F S L E K O N H D N G C T P T I O P L M D L D C F N

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

1 H N

1 H N A P K Q G A N C E M C B G N S O D S Q E F H L Q B G S G O J D N

1 H N A R A B I P J C N O F G Q E I H E N D F M K I N

1 H N B F B O B G K I G C O A I O F T O B G D L I E A D B A Q I N

1 H N B F K I P M Q N

1 H N K P R M Q T I K N M A I N T N

1 H N K D G N S G O K S O P M R F R I D L B G L S G J G Q D H Q O Q C K H Q N

1 H N L Q C B D A N O C N G A D B C D P M H E K I A P A S K J N

1 H N L E Q O T E N F L E S N D S N

1 H N M Q A F B N

1 H N M S C I B H D B Q B C E K I G I S N

1 H N M D B S T J D I E T O S N

1 H N M E L F I T Q G M T D O E I R O N

1 H N M F N K N

1 H N M J O E F E N M S P C A G N

1 H N O Q S L Q I R P B O I C Q M T M T N

1 H N O T R S I A G S N

1 H N O T H Q K N O E F B Q P G P Q L B A J N

1 H N P N

1 H N P J I D I E B D T K J A Q M O I J G M T H T J Q K R I Q N

1 H N Q K S G K J E T R B E C B P B T M Q N

1 H N Q M R N I K B C F P T O N D K D R E F I D I E C K S E N

1 H N Q N T S M J L E H P F T O F A N

1 H N Q O A D C N S Q S O I O C D J N

1 H N Q H L P Q N A Q F N C Q N D R Q L E N D G B O F Q G D P I N M I Q H N

1 H N Q H N R N

1 H N R P J L R G N M Q N

1 H N R D A S D J R C O H R T H R P T K E I N K J P O G M L G H L A M G P N

1 H N S A O A C A L H S I N F N

1 H N S L F L S N

1 H N S D O R G A L B F E O N K I T I M A E R N

1 H N S E J K T O R E N

1 H N S G K I Q M K R O G K D O H I J S N

1 H N S H S P M S T R S K C P S K B R P L N

1 H N T K J L S G D F N R L C I A I J D G F I L S M N M N

1 H N T F M J A H J Q F I K C K C D B O F N D E J B E N

1 H N T J M N

1 H N C S M R Q L E N M L S K D S O R M B P I N

1 H N C H B C P R K J H O K D S A G J L D R O L K O D E N

1 H N C J O K N C T P L C F S P H N K R O M B J A M J R O C J A P N

1 H N D R D M H I G N J N Q L K E T M A H E K B K N F Q K N

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

1 H N E K R T J T O I A C G E F R P G H T H D R C Q G F D N

1 H N E O E F G Q T M Q G J A I N

1 H N E R F R S I A R G B A M D G E F J P E M E F N

1 H N E F O G P M D K N D S K C B G R G S J D N

1 H N F O C D H J O R I G A J F C S M N T A N L T S H S I G O F N

1 H N F T C O M S I R P I B M N B H B S N

1 H N F C S C J A S L N

1 H N F D L F K C H E S M O P B H P I G O F B P O D T B D S M A S F N

1 H N G T G E P N Q A C Q F G C E S T N

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