Results of the Intermediate Node Algorithm on a Graph with a Central Bridge

The following connected, undirected graph has six bridges. A bridge is an edge whose removal disconnects the graph. This graph is interesting due to the "bottle-neck" edge, G, N. The edges to the leaf nodes (nodes with a degree of one - A, D, H, Q, T), are also bridges since the removal of the one incident would disconnect the graph. However, our focus is on the bridge between node G and node N. The topology of this graph is NOT likely to be typical, but we wanted to analyze each of the algorithms under such conditions.

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 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.

The following tables display the results obtained from 1000 executions of two cases. The first set of tables corresponds to 1000 executions where E is the source node communicating with various destination nodes, and the second set of tables corresponds to 1000 executions where N is the source node communicating with various destination nodes. Each table shows the number of times a given path was selected for a source to communicate with a destination node. It also shows the actual path taken. Note, the actual path displayed is shown in reverse order (destination to source).

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 syverson@itd.nrl.navy.mil and it will be included.

SOURCE E TO DESTINATION F:

FREQUENCY	PATH
6	F B A B E
10	F B A B F I E
11	F B C B E
12	F B E
10	F B F I E
28	F K F E
11	F K G N L N G C F E
9	F K G N O M O N G C F E
10	F K G N O N G C B E
9	F K G N O N G C F E
11	F K G N O P O N G C B E
16	F K G N O P O N G C F E
13	F K G N O P Q P O N G C B E
9	F K G N O P Q P O N G C F E
11	F K G N O P S P O N G C F E
12	F K G N R L M L R N G C B E
11	F K G N R L R N G C B E
5	F K G N R N G C B E
7	F K G N R N G C F E
15	F K G N R T R N G C B E
10	F K G N R T R N G C F E
13	F K G N S N G C B E
11	F K G N G C B E
11	F K G N G C F E
8	F K G C B E
13	F K G C F E
10	F C K C F E
32	F C F E
10	F C F I E
10	F C G N R L R N G C F E
11	F C G N R N G C F E
5	F C G N R T R N G C F E
18	F C G N S N G C F E
13	F C G N S O M L R N G C F E
11	F C G N S O M P M L R N G C F E
15	F C G N S O M P Q P M L R N G C F E
6	F C G N S O S N G C F E
1	F C G N S P M P S N G C F B E
13	F C G N G C F E
8	F C G C F E
32	F E B A B E
15	F E B C B E
10	F E B C G N L N G C B E
10	F E B C G N R N G C B E
15	F E B C G N R T R N G C B E
5	F E B C G N S N G C B E
15	F E B C G N S O S N G C B E
10	F E B C G N S P M P S N G C B E
13	F E B C G N S P Q P S N G C B E
12	F E B C G N S P S N G C B E
12	F E B C G N G C B E
4	F E B C G C B E
28	F E B E
43	F E D E
1	F E I E
21	F I E
15	F I E D E
28	F I F E
30	F I H I E
24	F I H I F E
9	F I J K G K J I E
14	F I J K G N L M L N G K J I E
8	F I J K G N L M P M L N G K J I E
17	F I J K G N L M P Q P M L N G K J I E
14	F I J K G N L N G K J I E
6	F I J K G N L R L N G K J I E
12	F I J K G N L R T R L N G K J I E
12	F I J K G N O N G K J I E
8	F I J K G N S N G K J I E
10	F I J K G N G K J I E
7	F I J K J I E
12	F I J I E
14	F J K J F E
34	F J F E
8	F J I E
10	F J I H I J F E
7	F J I J F E

SOURCE E TO DESTINATION G:

FREQUENCY	PATH
11	G K C B A B F I E
9	G K C B F I E
10	G K C F I E
36	G K F E
9	G K F I E
17	G K F I H I E
8	G K F J I E
22	G K J F E
32	G K J I E
15	G K J I E D E
12	G K J I F I E
15	G K J I H I E
14	G N L M L N G K J I E
9	G N L M P M L N G K J I E
16	G N L M P Q P M L N G K J I E
11	G N L N G K J I E
10	G N L N G C B E
10	G N L N G C F E
6	G N L R L N G K J I E
11	G N L R T R L N G K J I E
9	G N O M O N G C F E
10	G N O N G K J I E
10	G N O N G C B E
10	G N O N G C F E
13	G N O P O N G C B E
16	G N O P O N G C F E
13	G N O P Q P O N G C B E
8	G N O P Q P O N G C F E
10	G N O P S P O N G C F E
12	G N R L M L R N G C B E
12	G N R L R N G C B E
8	G N R L R N G C F E
14	G N R N G C B E
20	G N R N G C F E
30	G N R T R N G C B E
12	G N R T R N G C F E
9	G N S N G K J I E
18	G N S N G C B E
17	G N S N G C F E
12	G N S O M L R N G C F E
9	G N S O M P M L R N G C F E
15	G N S O M P Q P M L R N G C F E
13	G N S O S N G C B E
7	G N S O S N G C F E
8	G N S P M P S N G C B E
1	G N S P M P S N G C F B E
14	G N S P Q P S N G C B E
10	G N S P S N G C B E
9	G N G K J I E
23	G N G C B E
24	G N G C F E
17	G C B A B E
46	G C B E
21	G C B E D E
14	G C B E F E
13	G C B E F I F E
11	G C B E F I H I F E
10	G C K C F E
1	G C K F I H I E
1	G C K J I E
56	G C F E
21	G C F E B A B E
22	G C F E B E
22	G C F E D E
12	G C F I F E
12	G C F I H I F E
24	G C F J F E
12	G C F J I H I J F E
6	G C F J I J F E

SOURCE E TO DESTINATION H:

FREQUENCY	PATH
21	H I E
28	H I E D E
7	H I F B A B E
12	H I F B A B F I E
13	H I F B C B E
11	H I F B E
11	H I F B F I E
1	H I F K C G N L R L N G C K F B E
33	H I F K F E
9	H I F K G N L N G C F E
9	H I F K G N O M O N G C F E
11	H I F K G N O N G C B E
8	H I F K G N O N G C F E
14	H I F K G N O P O N G C B E
15	H I F K G N O P O N G C F E
12	H I F K G N O P Q P O N G C B E
9	H I F K G N O P Q P O N G C F E
11	H I F K G N O P S P O N G C F E
14	H I F K G N R L M L R N G C B E
11	H I F K G N R L R N G C B E
6	H I F K G N R N G C B E
10	H I F K G N R N G C F E
14	H I F K G N R T R N G C B E
9	H I F K G N R T R N G C F E
13	H I F K G N S N G C B E
11	H I F K G N G C B E
11	H I F K G N G C F E
9	H I F K G C B E
12	H I F K G C F E
15	H I F C F E
11	H I F C F I E
1	H I F C G N S P M P S N G C F B E
1	H I F C G C F E
54	H I F E
19	H I F E B A B E
15	H I F E B C B E
11	H I F E B C G N L N G C B E
9	H I F E B C G N R N G C B E
16	H I F E B C G N R T R N G C B E
9	H I F E B C G N S N G C B E
14	H I F E B C G N S O S N G C B E
8	H I F E B C G N S P M P S N G C B E
16	H I F E B C G N S P Q P S N G C B E
9	H I F E B C G N S P S N G C B E
12	H I F E B C G N G C B E
5	H I F E B C G C B E
21	H I F E B E
22	H I F E D E
12	H I F I E
10	H I F J F E
10	H I J K G K J I E
13	H I J K G N L M L N G K J I E
10	H I J K G N L M P M L N G K J I E
17	H I J K G N L M P Q P M L N G K J I E
12	H I J K G N L N G K J I E
8	H I J K G N L R L N G K J I E
10	H I J K G N L R T R L N G K J I E
9	H I J K G N O N G K J I E
9	H I J K G N S N G K J I E
1	H I J K G N S N G C F E
9	H I J K G N G K J I E
12	H I J K J F E
7	H I J K J I E
10	H I J F C K C F E
19	H I J F C F E
9	H I J F C G N R L R N G C F E
10	H I J F C G N R N G C F E
3	H I J F C G N R T R N G C F E
15	H I J F C G N S N G C F E
10	H I J F C G N S O M L R N G C F E
8	H I J F C G N S O M P M L R N G C F E
16	H I J F C G N S O M P Q P M L R N G C F E
9	H I J F C G N S O S N G C F E
16	H I J F C G N G C F E
8	H I J F C G C F E
41	H I J F E
13	H I J F E B A B E
11	H I J F E B E
9	H I J F E D E
21	H I J I E

SOURCE E TO DESTINATION I:

FREQUENCY	PATH
1	I E B E
25	I E D E
7	I F B A B E
10	I F B A B F I E
12	I F B C B E
13	I F B E
7	I F B F I E
28	I F K F E
10	I F K G N L N G C F E
9	I F K G N O M O N G C F E
9	I F K G N O N G C B E
8	I F K G N O N G C F E
12	I F K G N O P O N G C B E
15	I F K G N O P O N G C F E
11	I F K G N O P Q P O N G C B E
9	I F K G N O P Q P O N G C F E
12	I F K G N O P S P O N G C F E
12	I F K G N R L M L R N G C B E
13	I F K G N R L R N G C B E
5	I F K G N R N G C B E
12	I F K G N R N G C F E
14	I F K G N R T R N G C B E
8	I F K G N R T R N G C F E
12	I F K G N S N G C B E
10	I F K G N G C B E
11	I F K G N G C F E
10	I F K G C B E
12	I F K G C F E
14	I F C F E
10	I F C F I E
1	I F C G N S P M P S N G C F B E
1	I F C G C F E
29	I F E
18	I F E B A B E
13	I F E B C B E
10	I F E B C G N L N G C B E
9	I F E B C G N R N G C B E
18	I F E B C G N R T R N G C B E
9	I F E B C G N S N G C B E
15	I F E B C G N S O S N G C B E
9	I F E B C G N S P M P S N G C B E
17	I F E B C G N S P Q P S N G C B E
9	I F E B C G N S P S N G C B E
13	I F E B C G N G C B E
5	I F E B C G C B E
24	I F E B E
23	I F E D E
11	I F I E
9	I F J F E
35	I H I E
24	I H I F E
11	I H I J F E
9	I J K G K J I E
12	I J K G N L M L N G K J I E
10	I J K G N L M P M L N G K J I E
15	I J K G N L M P Q P M L N G K J I E
12	I J K G N L N G K J I E
7	I J K G N L R L N G K J I E
10	I J K G N L R T R L N G K J I E
12	I J K G N O N G K J I E
11	I J K G N S N G K J I E
1	I J K G N S N G C F E
9	I J K G N G K J I E
12	I J K J F E
11	I J K J I E
10	I J F C K C F E
20	I J F C F E
10	I J F C G N R L R N G C F E
10	I J F C G N R N G C F E
3	I J F C G N R T R N G C F E
13	I J F C G N S N G C F E
10	I J F C G N S O M L R N G C F E
8	I J F C G N S O M P M L R N G C F E
16	I J F C G N S O M P Q P M L R N G C F E
8	I J F C G N S O S N G C F E
13	I J F C G N G C F E
8	I J F C G C F E
32	I J F E
12	I J F E B A B E
11	I J F E B E
10	I J F E D E
21	I J I E

SOURCE E TO DESTINATION J:

FREQUENCY	PATH
11	J K C B A B E
30	J K C B E
11	J K C F I E
9	J K G K J I E
11	J K G N L M L N G K J I E
12	J K G N L M P M L N G K J I E
15	J K G N L M P Q P M L N G K J I E
12	J K G N L N G K J I E
11	J K G N L N G C B E
8	J K G N L R L N G K J I E
10	J K G N L R T R L N G K J I E
11	J K G N O N G K J I E
8	J K G N R N G C B E
15	J K G N R T R N G C B E
9	J K G N S N G K J I E
11	J K G N S N G C B E
1	J K G N S N G C F E
14	J K G N S O S N G C B E
8	J K G N S P M P S N G C B E
1	J K G N S P M P S N G C F B E
17	J K G N S P Q P S N G C B E
9	J K G N S P S N G C B E
9	J K G N G K J I E
12	J K G N G C B E
5	J K G C B E
9	J K J F E
8	J K J I E
6	J F B A B E
14	J F B C B E
13	J F B E
27	J F K F E
8	J F K G N L N G C F E
9	J F K G N O M O N G C F E
11	J F K G N O N G C B E
8	J F K G N O N G C F E
13	J F K G N O P O N G C B E
15	J F K G N O P O N G C F E
12	J F K G N O P Q P O N G C B E
11	J F K G N O P Q P O N G C F E
12	J F K G N O P S P O N G C F E
11	J F K G N R L M L R N G C B E
13	J F K G N R L R N G C B E
5	J F K G N R N G C B E
11	J F K G N R N G C F E
14	J F K G N R T R N G C B E
7	J F K G N R T R N G C F E
13	J F K G N S N G C B E
8	J F K G N G C B E
13	J F K G N G C F E
10	J F K G C B E
11	J F K G C F E
10	J F C K C F E
32	J F C F E
13	J F C G N R L R N G C F E
12	J F C G N R N G C F E
7	J F C G N R T R N G C F E
14	J F C G N S N G C F E
11	J F C G N S O M L R N G C F E
8	J F C G N S O M P M L R N G C F E
18	J F C G N S O M P Q P M L R N G C F E
8	J F C G N S O S N G C F E
13	J F C G N G C F E
7	J F C G C F E
37	J F E
19	J F E B A B E
25	J F E B E
29	J F E D E
10	J F I F E
13	J F I H I F E
22	J I E
30	J I E D E
12	J I F B A B F I E
6	J I F B F I E
9	J I F E
9	J I F I E
34	J I H I E
12	J I H I F E
11	J I H I J F E
7	J I J F E

SOURCE E TO DESTINATION K:

FREQUENCY	PATH
12	K C B A B E
10	K C B A B F I E
44	K C B E
8	K C B F I E
26	K C F E
15	K C F E B A B E
11	K C F E B E
10	K C F E D E
13	K C F I E
13	K C F J F E
11	K C F J I H I J F E
6	K C F J I J F E
13	K C G N R L R N G C F E
10	K C G N R N G C F E
5	K C G N R T R N G C F E
14	K C G N S N G C F E
11	K C G N S O M L R N G C F E
10	K C G N S O M P M L R N G C F E
17	K C G N S O M P Q P M L R N G C F E
8	K C G N S O S N G C F E
12	K C G N G C F E
7	K C G C F E
6	K F B A B E
14	K F B E
14	K F C F E
16	K F E
7	K F E B A B E
13	K F E B E
23	K F E D E
6	K F I E
10	K F I F E
18	K F I H I E
14	K F I H I F E
9	K F J F E
11	K F J I E
9	K G K J I E
10	K G N L M L N G K J I E
11	K G N L M P M L N G K J I E
15	K G N L M P Q P M L N G K J I E
11	K G N L N G K J I E
9	K G N L N G C B E
9	K G N L N G C F E
8	K G N L R L N G K J I E
10	K G N L R T R L N G K J I E
8	K G N O M O N G C F E
11	K G N O N G K J I E
11	K G N O N G C B E
11	K G N O N G C F E
12	K G N O P O N G C B E
14	K G N O P O N G C F E
11	K G N O P Q P O N G C B E
9	K G N O P Q P O N G C F E
13	K G N O P S P O N G C F E
12	K G N R L M L R N G C B E
13	K G N R L R N G C B E
14	K G N R N G C B E
14	K G N R N G C F E
29	K G N R T R N G C B E
8	K G N R T R N G C F E
10	K G N S N G K J I E
25	K G N S N G C B E
1	K G N S N G C F E
14	K G N S O S N G C B E
9	K G N S P M P S N G C B E
1	K G N S P M P S N G C F B E
15	K G N S P Q P S N G C B E
10	K G N S P S N G C B E
10	K G N G K J I E
23	K G N G C B E
13	K G N G C F E
17	K G C B E
12	K G C F E
16	K J F E
8	K J F E D E
21	K J I E
17	K J I E D E
9	K J I F E
11	K J I F I E
15	K J I H I E
14	K J I H I F E

SOURCE E TO DESTINATION L:

FREQUENCY	PATH
9	L M L N G K J I E
10	L M L R N G C B E
12	L M L R N G C F E
11	L M O N G C B E
8	L M O N G C F E
8	L M O S N G C F E
12	L M P M L N G K J I E
9	L M P M L R N G C F E
14	L M P O N G C B E
14	L M P Q P M L N G K J I E
21	L M P Q P M L R N G C F E
10	L M P Q P O N G C B E
15	L M P Q P S N G C B E
11	L M P S N G K J I E
18	L M P S N G C B E
1	L M P S N G C F B E
11	L N O N G K J I E
9	L N O N G C F E
13	L N O P O N G C F E
11	L N O P Q P O N G C F E
11	L N O P S P O N G C F E
10	L N R N G C F E
7	L N R T R N G C F E
12	L N S N G C B E
1	L N S N G C F E
12	L N S O S N G C B E
10	L N G K C B A B F I E
7	L N G K C B F I E
11	L N G K C F I E
13	L N G K F E
19	L N G K J F E
52	L N G K J I E
17	L N G K J I E D E
11	L N G K J I F I E
16	L N G K J I H I E
12	L N G C B A B E
48	L N G C B E
8	L N G C B E D E
11	L N G C B E F E
7	L N G C B E F I F E
13	L N G C B E F I H I F E
1	L N G C K F I H I E
1	L N G C K J I E
48	L N G C F E
9	L N G C F E B A B E
14	L N G C F E B E
14	L N G C F E D E
9	L N G C F I F E
16	L N G C F I H I F E
8	L N G C F J F E
7	L R L N G K J I E
13	L R N S N G C B E
15	L R N S N G C F E
22	L R N G K F E
6	L R N G K F I E
14	L R N G K F I H I E
11	L R N G K F J I E
6	L R N G C B A B E
65	L R N G C B E
12	L R N G C B E D E
11	L R N G C K C F E
53	L R N G C F E
15	L R N G C F E B A B E
10	L R N G C F E B E
9	L R N G C F E D E
14	L R N G C F J F E
11	L R N G C F J I H I J F E
6	L R N G C F J I J F E
11	L R T R L N G K J I E
29	L R T R N G C B E
5	L R T R N G C F E

SOURCE E TO DESTINATION M:

FREQUENCY	PATH
11	M L N G K C B A B F I E
6	M L N G K C B F I E
10	M L N G K C F I E
60	M L N G K J I E
16	M L N G K J I E D E
12	M L N G K J I F I E
19	M L N G K J I H I E
9	M L N G C B E
1	M L N G C K F I H I E
1	M L N G C K J I E
8	M L N G C F E
8	M L R L N G K J I E
21	M L R N G K F E
8	M L R N G K F I E
14	M L R N G K F I H I E
12	M L R N G K F J I E
11	M L R N G C B A B E
59	M L R N G C B E
11	M L R N G C B E D E
10	M L R N G C K C F E
1	M L R N G C F B E
70	M L R N G C F E
17	M L R N G C F E B A B E
11	M L R N G C F E B E
9	M L R N G C F E D E
14	M L R N G C F J F E
9	M L R N G C F J I H I J F E
8	M L R N G C F J I J F E
10	M L R T R L N G K J I E
14	M L R T R N G C B E
4	M L R T R N G C F E
10	M O N R N G C F E
8	M O N R T R N G C F E
12	M O N G K F E
11	M O N G K J I E
13	M O N G C B E
61	M O N G C F E
10	M O N G C F E B A B E
15	M O N G C F E B E
13	M O N G C F E D E
8	M O N G C F I F E
15	M O N G C F I H I F E
7	M O N G C F J F E
12	M O P O N G C F E
10	M O P Q P O N G C F E
11	M O P S P O N G C F E
12	M O S N G C B E
21	M O S N G C F E
11	M P M L N G K J I E
9	M P M L R N G C F E
15	M P O N G C B E
14	M P Q P M L N G K J I E
17	M P Q P M L R N G C F E
10	M P Q P O N G C B E
14	M P Q P S N G C B E
7	M P S N R N G C B E
16	M P S N R T R N G C B E
16	M P S N G K J F E
11	M P S N G K J I E
11	M P S N G C B A B E
75	M P S N G C B E
9	M P S N G C B E D E
11	M P S N G C B E F E
9	M P S N G C B E F I F E
12	M P S N G C B E F I H I F E
10	M P S O S N G C B E

SOURCE E TO DESTINATION N:

FREQUENCY	PATH
8	N L M L N G K J I E
9	N L M P M L N G K J I E
11	N L M P Q P M L N G K J I E
12	N L N G K J I E
9	N L N G C B E
10	N L N G C F E
8	N L R L N G K J I E
11	N L R T R L N G K J I E
10	N O M O N G C F E
13	N O N G K J I E
11	N O N G C B E
9	N O N G C F E
13	N O P O N G C B E
12	N O P O N G C F E
9	N O P Q P O N G C B E
11	N O P Q P O N G C F E
13	N O P S P O N G C F E
12	N R L M L R N G C B E
9	N R L R N G C B E
13	N R L R N G C F E
13	N R N G C B E
19	N R N G C F E
29	N R T R N G C B E
12	N R T R N G C F E
11	N S N G K J I E
26	N S N G C B E
16	N S N G C F E
11	N S O M L R N G C F E
8	N S O M P M L R N G C F E
19	N S O M P Q P M L R N G C F E
10	N S O S N G C B E
8	N S O S N G C F E
9	N S P M P S N G C B E
1	N S P M P S N G C F B E
15	N S P Q P S N G C B E
9	N S P S N G C B E
10	N G K C B A B F I E
8	N G K C B F I E
9	N G K C F I E
35	N G K F E
9	N G K F I E
15	N G K F I H I E
13	N G K F J I E
17	N G K J F E
41	N G K J I E
17	N G K J I E D E
13	N G K J I F I E
18	N G K J I H I E
20	N G C B A B E
79	N G C B E
19	N G C B E D E
12	N G C B E F E
8	N G C B E F I F E
13	N G C B E F I H I F E
10	N G C K C F E
1	N G C K J I E
68	N G C F E
26	N G C F E B A B E
25	N G C F E B E
21	N G C F E D E
7	N G C F I F E
17	N G C F I H I F E
22	N G C F J F E
11	N G C F J I H I J F E
7	N G C F J I J F E

SOURCE E TO DESTINATION O:

FREQUENCY	PATH
8	O M L N G K J I E
1	O M L N G C K J I E
11	O M L R N G C B E
39	O M L R N G C F E
7	O M L R T R N G C F E
8	O M O N G C F E
12	O M P M L R N G C F E
18	O M P Q P M L R N G C F E
1	O M P S N G C F B E
11	O N L N G K J I E
9	O N L N G C F E
7	O N L R L N G K J I E
14	O N L R T R L N G K J I E
10	O N R L R N G C B E
5	O N R N G C B E
12	O N R N G C F E
14	O N R T R N G C B E
6	O N R T R N G C F E
11	O N G K C B A B F I E
7	O N G K C B F I E
10	O N G K C F I E
36	O N G K F E
7	O N G K F I E
14	O N G K F I H I E
14	O N G K F J I E
1	O N G K J F E
48	O N G K J I E
18	O N G K J I E D E
12	O N G K J I F I E
17	O N G K J I H I E
12	O N G C B A B E
43	O N G C B E
11	O N G C B E D E
50	O N G C F E
10	O N G C F E B A B E
14	O N G C F E B E
13	O N G C F E D E
7	O N G C F I F E
15	O N G C F I H I F E
7	O N G C F J F E
15	O P O N G C B E
12	O P O N G C F E
8	O P Q P O N G C B E
12	O P Q P O N G C F E
13	O P S P O N G C F E
11	O S N L N G C B E
8	O S N R N G C B E
13	O S N R T R N G C B E
18	O S N G K J F E
12	O S N G K J I E
12	O S N G C B A B E
77	O S N G C B E
8	O S N G C B E D E
12	O S N G C B E F E
8	O S N G C B E F I F E
13	O S N G C B E F I H I F E
8	O S N G C K C F E
53	O S N G C F E
15	O S N G C F E B A B E
11	O S N G C F E B E
6	O S N G C F E D E
10	O S N G C F J F E
12	O S N G C F J I H I J F E
8	O S N G C F J I J F E
12	O S P M L N G K J I E
9	O S P M P S N G C B E
12	O S P Q P M L N G K J I E
15	O S P Q P S N G C B E
7	O S P S N G C B E

SOURCE E TO DESTINATION P:

FREQUENCY	PATH
10	P M L N G K C B A B F I E
9	P M L N G K C B F I E
11	P M L N G K C F I E
69	P M L N G K J I E
17	P M L N G K J I E D E
12	P M L N G K J I F I E
17	P M L N G K J I H I E
10	P M L N G C B E
8	P M L R L N G K J I E
21	P M L R N G C B E
9	P M L R N G C K C F E
83	P M L R N G C F E
16	P M L R N G C F E B A B E
10	P M L R N G C F E B E
6	P M L R N G C F E D E
11	P M L R N G C F J F E
13	P M L R N G C F J I H I J F E
8	P M L R N G C F J I J F E
11	P M L R T R L N G K J I E
7	P M L R T R N G C F E
20	P M O S N G C F E
9	P M P S N G C B E
1	P M P S N G C F B E
7	P O M O N G C F E
10	P O N L N G C F E
5	P O N R N G C B E
11	P O N R N G C F E
12	P O N R T R N G C B E
5	P O N R T R N G C F E
35	P O N G K F E
7	P O N G K F I E
14	P O N G K F I H I E
16	P O N G K F J I E
1	P O N G K J F E
10	P O N G C B A B E
58	P O N G C B E
12	P O N G C B E D E
60	P O N G C F E
12	P O N G C F E B A B E
14	P O N G C F E B E
14	P O N G C F E D E
5	P O N G C F I F E
14	P O N G C F I H I F E
10	P O N G C F J F E
13	P O S N G C B E
10	P Q P M L N G K J I E
16	P Q P M L R N G C F E
8	P Q P O N G C B E
10	P Q P O N G C F E
15	P Q P S N G C B E
5	P S N R N G C B E
13	P S N R T R N G C B E
17	P S N G K J F E
11	P S N G K J I E
14	P S N G C B A B E
62	P S N G C B E
9	P S N G C B E D E
11	P S N G C B E F E
9	P S N G C B E F I F E
14	P S N G C B E F I H I F E
1	P S N G C K J I E
1	P S N G C F E
14	P S O N G K J I E
12	P S O S N G C B E
15	P S P O N G C F E

SOURCE E TO DESTINATION Q:

FREQUENCY	PATH
10	Q P M L N G K C B A B F I E
8	Q P M L N G K C B F I E
11	Q P M L N G K C F I E
77	Q P M L N G K J I E
18	Q P M L N G K J I E D E
11	Q P M L N G K J I F I E
17	Q P M L N G K J I H I E
11	Q P M L N G C B E
9	Q P M L R L N G K J I E
18	Q P M L R N G C B E
9	Q P M L R N G C K C F E
93	Q P M L R N G C F E
16	Q P M L R N G C F E B A B E
11	Q P M L R N G C F E B E
8	Q P M L R N G C F E D E
10	Q P M L R N G C F J F E
13	Q P M L R N G C F J I H I J F E
10	Q P M L R N G C F J I J F E
12	Q P M L R T R L N G K J I E
7	Q P M L R T R N G C F E
22	Q P M O S N G C F E
8	Q P M P S N G C B E
1	Q P M P S N G C F B E
8	Q P O M O N G C F E
9	Q P O N L N G C F E
6	Q P O N R N G C B E
10	Q P O N R N G C F E
11	Q P O N R T R N G C B E
6	Q P O N R T R N G C F E
37	Q P O N G K F E
7	Q P O N G K F I E
13	Q P O N G K F I H I E
14	Q P O N G K F J I E
1	Q P O N G K J F E
10	Q P O N G C B A B E
74	Q P O N G C B E
9	Q P O N G C B E D E
68	Q P O N G C F E
13	Q P O N G C F E B A B E
15	Q P O N G C F E B E
14	Q P O N G C F E D E
6	Q P O N G C F I F E
15	Q P O N G C F I H I F E
8	Q P O N G C F J F E
13	Q P O S N G C B E
8	Q P S N R N G C B E
12	Q P S N R T R N G C B E
18	Q P S N G K J F E
11	Q P S N G K J I E
13	Q P S N G C B A B E
71	Q P S N G C B E
11	Q P S N G C B E D E
12	Q P S N G C B E F E
11	Q P S N G C B E F I F E
12	Q P S N G C B E F I H I F E
1	Q P S N G C K J I E
1	Q P S N G C F E
15	Q P S O N G K J I E
13	Q P S O S N G C B E
14	Q P S P O N G C F E

SOURCE E TO DESTINATION R:

FREQUENCY	PATH
9	R L M L N G K J I E
10	R L M L R N G C B E
16	R L M L R N G C F E
6	R L M O S N G C F E
11	R L M P M L N G K J I E
13	R L M P M L R N G C F E
10	R L M P Q P M L N G K J I E
14	R L M P Q P M L R N G C F E
14	R L M P S N G K J I E
1	R L M P S N G C F B E
14	R L N O N G K J I E
9	R L N G K C B A B F I E
6	R L N G K C B F I E
11	R L N G K C F I E
1	R L N G K F I E
59	R L N G K J I E
18	R L N G K J I E D E
12	R L N G K J I F I E
15	R L N G K J I H I E
11	R L N G C B E
1	R L N G C K J I E
10	R L R N G C B E
17	R L R N G C F E
8	R N L N G C F E
12	R N O M O N G C F E
11	R N O N G C B E
8	R N O N G C F E
13	R N O P O N G C B E
12	R N O P O N G C F E
5	R N O P Q P O N G C B E
12	R N O P Q P O N G C F E
12	R N O P S P O N G C F E
25	R N S N G C B E
13	R N S N G C F E
12	R N S O S N G C B E
8	R N S P M P S N G C B E
15	R N S P Q P S N G C B E
5	R N S P S N G C B E
38	R N G K F E
8	R N G K F I E
11	R N G K F I H I E
14	R N G K F J I E
20	R N G K J F E
23	R N G C B A B E
99	R N G C B E
20	R N G C B E D E
9	R N G C B E F E
10	R N G C B E F I F E
12	R N G C B E F I H I F E
7	R N G C K C F E
86	R N G C F E
31	R N G C F E B A B E
26	R N G C F E B E
20	R N G C F E D E
7	R N G C F I F E
15	R N G C F I H I F E
17	R N G C F J F E
12	R N G C F J I H I J F E
10	R N G C F J I J F E
11	R T R L N G K J I E
23	R T R N G C B E
12	R T R N G C F E

SOURCE E TO DESTINATION S:

FREQUENCY	PATH
11	S N L N G C B E
11	S N R L R N G C B E
17	S N R N G C B E
9	S N R N G C F E
22	S N R T R N G C B E
7	S N R T R N G C F E
7	S N G K C B A B F I E
8	S N G K C B F I E
12	S N G K C F I E
22	S N G K F E
9	S N G K F I E
12	S N G K F I H I E
16	S N G K F J I E
20	S N G K J F E
49	S N G K J I E
17	S N G K J I E D E
15	S N G K J I F I E
17	S N G K J I H I E
22	S N G C B A B E
101	S N G C B E
24	S N G C B E D E
9	S N G C B E F E
9	S N G C B E F I F E
11	S N G C B E F I H I F E
6	S N G C K C F E
1	S N G C K J F E
46	S N G C F E
15	S N G C F E B A B E
11	S N G C F E B E
7	S N G C F E D E
9	S N G C F J F E
12	S N G C F J I H I J F E
10	S N G C F J I J F E
12	S O M L R N G C B E
31	S O M L R N G C F E
14	S O M P M L R N G C F E
15	S O M P Q P M L R N G C F E
1	S O N G K F I E
14	S O N G K J I E
11	S O N G C B E
14	S O P O N G C B E
5	S O P Q P O N G C B E
14	S O S N G C B E
7	S O S N G C F E
28	S P M L N G K J I E
9	S P M L R L N G K J I E
12	S P M L R T R L N G K J I E
8	S P M P S N G C B E
9	S P O M O N G C F E
9	S P O N L N G C F E
12	S P O N R N G C F E
7	S P O N R T R N G C F E
10	S P O N G K F E
68	S P O N G C F E
14	S P O N G C F E B A B E
15	S P O N G C F E B E
13	S P O N G C F E D E
8	S P O N G C F I F E
15	S P O N G C F I H I F E
8	S P O N G C F J F E
11	S P Q P M L N G K J I E
11	S P Q P O N G C F E
17	S P Q P S N G C B E
4	S P S N G C B E

SOURCE E TO DESTINATION T:

FREQUENCY	PATH
6	T R L M L N G K J I E
11	T R L M L R N G C B E
15	T R L M L R N G C F E
7	T R L M O S N G C F E
11	T R L M P M L N G K J I E
15	T R L M P M L R N G C F E
9	T R L M P Q P M L N G K J I E
15	T R L M P Q P M L R N G C F E
13	T R L M P S N G K J I E
17	T R L N O N G K J I E
7	T R L N G K C B A B F I E
7	T R L N G K C B F I E
14	T R L N G K C F I E
1	T R L N G K F I E
71	T R L N G K J I E
14	T R L N G K J I E D E
14	T R L N G K J I F I E
16	T R L N G K J I H I E
13	T R L N G C B E
11	T R L R N G C B E
15	T R L R N G C F E
8	T R N L N G C F E
9	T R N O M O N G C F E
1	T R N O N G K F I E
12	T R N O N G C B E
9	T R N O N G C F E
13	T R N O P O N G C B E
12	T R N O P O N G C F E
5	T R N O P Q P O N G C B E
11	T R N O P Q P O N G C F E
12	T R N O P S P O N G C F E
25	T R N S N G C B E
12	T R N S N G C F E
12	T R N S O S N G C B E
9	T R N S P M P S N G C B E
11	T R N S P Q P S N G C B E
4	T R N S P S N G C B E
34	T R N G K F E
7	T R N G K F I E
11	T R N G K F I H I E
17	T R N G K F J I E
23	T R N G K J F E
23	T R N G C B A B E
116	T R N G C B E
23	T R N G C B E D E
8	T R N G C B E F E
9	T R N G C B E F I F E
12	T R N G C B E F I H I F E
9	T R N G C K C F E
1	T R N G C K J F E
106	T R N G C F E
27	T R N G C F E B A B E
26	T R N G C F E B E
20	T R N G C F E D E
9	T R N G C F I F E
15	T R N G C F I H I F E
15	T R N G C F J F E
12	T R N G C F J I H I J F E
10	T R N G C F J I J F E

SOURCE N TO DESTINATION O:

FREQUENCY	PATH
12	O M L N
44	O M L R N
14	O M L R T R N
11	O M O N
12	O M P M L R N
8	O M P Q P M L R N
18	O N L N
20	O N L R L N
7	O N L R T R L N
13	O N R L R N
26	O N R N
28	O N R T R N
11	O N G K C B A B C K G N
14	O N G K C B C K G N
10	O N G K C K G N
8	O N G K F K G N
1	O N G K F E F K G N
11	O N G K F I F K G N
15	O N G K F I H I F K G N
14	O N G K F J F K G N
29	O N G K G N
17	O N G K J K G N
8	O N G K J I E D E I J K G N
10	O N G K J I E I J K G N
13	O N G K J I F I J K G N
10	O N G K J I H I J K G N
9	O N G K J I J K G N
31	O N G N
11	O N G C B A B C G N
8	O N G C B C G N
10	O N G C B E B C G N
12	O N G C B E D E B C G N
13	O N G C F K G N
14	O N G C F E B A B E F K G N
9	O N G C F E B E F K G N
13	O N G C F E D E F K G N
14	O N G C F E F K G N
14	O N G C F I F K G N
8	O N G C F I H I F K G N
9	O N G C F J F K G N
24	O N G C G N
1	O P M L N
14	O P O N
19	O P Q P O N
8	O P S P O N
45	O S N
12	O S N L N
9	O S N R N
12	O S N R T R N
12	O S N G K G N
10	O S N G K J K G N
24	O S N G N
9	O S N G C B A B C G N
12	O S N G C B C G N
11	O S N G C B E B C G N
8	O S N G C B E D E B C G N
13	O S N G C B E F E B C G N
13	O S N G C B E F I F E B C G N
11	O S N G C B E F I H I F E B C G N
11	O S N G C K C G N
1	O S N G C K F B A B F K C G N
15	O S N G C F C G N
10	O S N G C F E B A B E F C G N
14	O S N G C F E B E F C G N
10	O S N G C F E D E F C G N
9	O S N G C F E F C G N
10	O S N G C F J F C G N
10	O S N G C F J I H I J F C G N
9	O S N G C F J I J F C G N
23	O S N G C G N
5	O S P M L N
8	O S P M P S N
11	O S P Q P M L N
19	O S P Q P S N
9	O S P S N

SOURCE N TO DESTINATION P:

FREQUENCY	PATH
36	P M L N
11	P M L N G K C B A B C K G N
14	P M L N G K C B C K G N
10	P M L N G K C K G N
9	P M L N G K G N
15	P M L N G K J K G N
6	P M L N G K J I E D E I J K G N
8	P M L N G K J I E I J K G N
12	P M L N G K J I F I J K G N
10	P M L N G K J I H I J K G N
8	P M L N G K J I J K G N
11	P M L N G N
18	P M L R L N
58	P M L R N
14	P M L R N G N
10	P M L R N G C K C G N
15	P M L R N G C F C G N
10	P M L R N G C F E B A B E F C G N
13	P M L R N G C F E B E F C G N
10	P M L R N G C F E D E F C G N
8	P M L R N G C F E F C G N
9	P M L R N G C F J F C G N
12	P M L R N G C F J I H I J F C G N
10	P M L R N G C F J I J F C G N
8	P M L R N G C G N
8	P M L R T R L N
16	P M L R T R N
22	P M O S N
7	P M P S N
12	P O M O N
17	P O N
8	P O N L N
26	P O N R N
29	P O N R T R N
6	P O N G K F K G N
1	P O N G K F E F K G N
12	P O N G K F I F K G N
15	P O N G K F I H I F K G N
14	P O N G K F J F K G N
14	P O N G K G N
19	P O N G N
10	P O N G C B A B C G N
9	P O N G C B C G N
11	P O N G C B E B C G N
11	P O N G C B E D E B C G N
13	P O N G C F K G N
14	P O N G C F E B A B E F K G N
9	P O N G C F E B E F K G N
15	P O N G C F E D E F K G N
14	P O N G C F E F K G N
14	P O N G C F I F K G N
10	P O N G C F I H I F K G N
10	P O N G C F J F K G N
22	P O N G C G N
11	P O S N
1	P O S N R N
10	P Q P M L N
11	P Q P M L R N
19	P Q P O N
20	P Q P S N
22	P S N
9	P S N R N
14	P S N R T R N
13	P S N G K G N
9	P S N G K J K G N
8	P S N G N
11	P S N G C B A B C G N
11	P S N G C B C G N
10	P S N G C B E B C G N
7	P S N G C B E D E B C G N
17	P S N G C B E F E B C G N
13	P S N G C B E F I F E B C G N
7	P S N G C B E F I H I F E B C G N
1	P S N G C K F B A B F K C G N
16	P S N G C G N
12	P S O N
7	P S O S N
8	P S P O N

SOURCE N TO DESTINATION Q:

FREQUENCY	PATH
42	Q P M L N
12	Q P M L N G K C B A B C K G N
14	Q P M L N G K C B C K G N
12	Q P M L N G K C K G N
9	Q P M L N G K G N
15	Q P M L N G K J K G N
6	Q P M L N G K J I E D E I J K G N
10	Q P M L N G K J I E I J K G N
12	Q P M L N G K J I F I J K G N
10	Q P M L N G K J I H I J K G N
11	Q P M L N G K J I J K G N
10	Q P M L N G N
18	Q P M L R L N
70	Q P M L R N
14	Q P M L R N G N
11	Q P M L R N G C K C G N
16	Q P M L R N G C F C G N
11	Q P M L R N G C F E B A B E F C G N
14	Q P M L R N G C F E B E F C G N
7	Q P M L R N G C F E D E F C G N
9	Q P M L R N G C F E F C G N
9	Q P M L R N G C F J F C G N
13	Q P M L R N G C F J I H I J F C G N
8	Q P M L R N G C F J I J F C G N
8	Q P M L R N G C G N
8	Q P M L R T R L N
14	Q P M L R T R N
23	Q P M O S N
6	Q P M P S N
8	Q P O M O N
32	Q P O N
7	Q P O N L N
24	Q P O N R N
28	Q P O N R T R N
7	Q P O N G K F K G N
10	Q P O N G K F I F K G N
17	Q P O N G K F I H I F K G N
13	Q P O N G K F J F K G N
15	Q P O N G K G N
21	Q P O N G N
12	Q P O N G C B A B C G N
11	Q P O N G C B C G N
10	Q P O N G C B E B C G N
12	Q P O N G C B E D E B C G N
13	Q P O N G C F K G N
13	Q P O N G C F E B A B E F K G N
12	Q P O N G C F E B E F K G N
13	Q P O N G C F E D E F K G N
16	Q P O N G C F E F K G N
15	Q P O N G C F I F K G N
8	Q P O N G C F I H I F K G N
11	Q P O N G C F J F K G N
21	Q P O N G C G N
13	Q P O S N
1	Q P O S N R N
30	Q P S N
7	Q P S N R N
15	Q P S N R T R N
16	Q P S N G K G N
10	Q P S N G K J K G N
11	Q P S N G N
10	Q P S N G C B A B C G N
10	Q P S N G C B C G N
14	Q P S N G C B E B C G N
8	Q P S N G C B E D E B C G N
15	Q P S N G C B E F E B C G N
12	Q P S N G C B E F I F E B C G N
10	Q P S N G C B E F I H I F E B C G N
1	Q P S N G C K F B A B F K C G N
17	Q P S N G C G N
12	Q P S O N
8	Q P S O S N
9	Q P S P O N

SOURCE N TO DESTINATION R:

FREQUENCY	PATH
13	R L M L N
21	R L M L R N
12	R L M O S N
5	R L M P M L N
11	R L M P M L R N
14	R L M P Q P M L N
11	R L M P Q P M L R N
11	R L M P S N
23	R L N
11	R L N O N
12	R L N G K C B A B C K G N
15	R L N G K C B C K G N
15	R L N G K C K G N
10	R L N G K G N
17	R L N G K J K G N
5	R L N G K J I E D E I J K G N
9	R L N G K J I E I J K G N
15	R L N G K J I F I J K G N
9	R L N G K J I H I J K G N
10	R L N G K J I J K G N
10	R L N G N
21	R L R N
7	R N L N
8	R N O M O N
13	R N O N
17	R N O P O N
23	R N O P Q P O N
10	R N O P S P O N
34	R N S N
9	R N S O S N
4	R N S P M P S N
17	R N S P Q P S N
11	R N S P S N
10	R N G K F K G N
8	R N G K F I F K G N
15	R N G K F I H I F K G N
14	R N G K F J F K G N
35	R N G K G N
10	R N G K J K G N
51	R N G N
21	R N G C B A B C G N
19	R N G C B C G N
20	R N G C B E B C G N
20	R N G C B E D E B C G N
16	R N G C B E F E B C G N
11	R N G C B E F I F E B C G N
8	R N G C B E F I H I F E B C G N
10	R N G C K C G N
1	R N G C K F B A B F K C G N
13	R N G C F K G N
15	R N G C F C G N
12	R N G C F E B A B E F K G N
10	R N G C F E B A B E F C G N
9	R N G C F E B E F K G N
15	R N G C F E B E F C G N
15	R N G C F E D E F K G N
10	R N G C F E D E F C G N
15	R N G C F E F K G N
8	R N G C F E F C G N
14	R N G C F I F K G N
8	R N G C F I H I F K G N
11	R N G C F J F K G N
10	R N G C F J F C G N
14	R N G C F J I H I J F C G N
9	R N G C F J I J F C G N
47	R N G C G N
7	R T R L N
56	R T R N

SOURCE N TO DESTINATION S:

FREQUENCY	PATH
14	S N L N
11	S N R L R N
35	S N R N
36	S N R T R N
12	S N G K C B A B C K G N
13	S N G K C B C K G N
12	S N G K C K G N
6	S N G K F K G N
9	S N G K F I F K G N
16	S N G K F I H I F K G N
16	S N G K F J F K G N
38	S N G K G N
27	S N G K J K G N
6	S N G K J I E D E I J K G N
9	S N G K J I E I J K G N
11	S N G K J I F I J K G N
8	S N G K J I H I J K G N
11	S N G K J I J K G N
46	S N G N
19	S N G C B A B C G N
19	S N G C B C G N
20	S N G C B E B C G N
21	S N G C B E D E B C G N
15	S N G C B E F E B C G N
12	S N G C B E F I F E B C G N
9	S N G C B E F I H I F E B C G N
11	S N G C K C G N
1	S N G C K F B A B F K C G N
13	S N G C F C G N
11	S N G C F E B A B E F C G N
16	S N G C F E B E F C G N
7	S N G C F E D E F C G N
9	S N G C F E F C G N
11	S N G C F J F C G N
14	S N G C F J I H I J F C G N
10	S N G C F J I J F C G N
35	S N G C G N
29	S O M L R N
11	S O M P M L R N
10	S O M P Q P M L R N
22	S O N
8	S O P O N
10	S O P Q P O N
20	S O S N
30	S P M L N
17	S P M L R L N
8	S P M L R T R L N
7	S P M P S N
7	S P O M O N
13	S P O N
7	S P O N L N
13	S P O N R N
16	S P O N R T R N
11	S P O N G K G N
12	S P O N G N
11	S P O N G C F K G N
13	S P O N G C F E B A B E F K G N
9	S P O N G C F E B E F K G N
15	S P O N G C F E D E F K G N
18	S P O N G C F E F K G N
14	S P O N G C F I F K G N
7	S P O N G C F I H I F K G N
12	S P O N G C F J F K G N
9	S P O N G C G N
12	S P Q P M L N
12	S P Q P O N
17	S P Q P S N
11	S P S N

SOURCE N TO DESTINATION T:

FREQUENCY	PATH
12	T R L M L N
25	T R L M L R N
11	T R L M O S N
3	T R L M P M L N
12	T R L M P M L R N
12	T R L M P Q P M L N
11	T R L M P Q P M L R N
10	T R L M P S N
44	T R L N
10	T R L N O N
14	T R L N G K C B A B C K G N
13	T R L N G K C B C K G N
12	T R L N G K C K G N
1	T R L N G K F I F K G N
9	T R L N G K G N
15	T R L N G K J K G N
7	T R L N G K J I E D E I J K G N
11	T R L N G K J I E I J K G N
13	T R L N G K J I F I J K G N
8	T R L N G K J I H I J K G N
11	T R L N G K J I J K G N
10	T R L N G N
1	T R L N G C G N
21	T R L R N
48	T R N
8	T R N L N
9	T R N O M O N
15	T R N O N
16	T R N O P O N
25	T R N O P Q P O N
8	T R N O P S P O N
32	T R N S N
9	T R N S O S N
5	T R N S P M P S N
16	T R N S P Q P S N
10	T R N S P S N
6	T R N G K F K G N
8	T R N G K F I F K G N
17	T R N G K F I H I F K G N
16	T R N G K F J F K G N
36	T R N G K G N
11	T R N G K J K G N
45	T R N G N
20	T R N G C B A B C G N
23	T R N G C B C G N
21	T R N G C B E B C G N
19	T R N G C B E D E B C G N
16	T R N G C B E F E B C G N
13	T R N G C B E F I F E B C G N
7	T R N G C B E F I H I F E B C G N
11	T R N G C K C G N
14	T R N G C F K G N
12	T R N G C F C G N
13	T R N G C F E B A B E F K G N
10	T R N G C F E B A B E F C G N
11	T R N G C F E B E F K G N
16	T R N G C F E B E F C G N
16	T R N G C F E D E F K G N
8	T R N G C F E D E F C G N
16	T R N G C F E F K G N
9	T R N G C F E F C G N
15	T R N G C F I F K G N
7	T R N G C F I H I F K G N
11	T R N G C F J F K G N
9	T R N G C F J F C G N
14	T R N G C F J I H I J F C G N
9	T R N G C F J I J F C G N
44	T R N G C G N

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