```
Cn cycle graph en.wikipedia.org/wiki/Cycle_graph
Kn complete graph en.wikipedia.org/wiki/Complete_graph
Km,n complete bipartite graph en.wikipedia.org/wiki/Complete_bipartite_graph
Pn path graph en.wikipedia.org/wiki/Path_graph
Wn wheel graph en.wikipedia.org/wiki/Wheel_graph

N T(N-1) graph #binary & hex matrix degrees images nicks isomorphicwith
1 0 1-0 [N/A] [N/A] 0  point; hermit; K1 1-0
2 1 2-0 00x0 BA0 0,0  two strangers 2-0
2 1 2-1 10x1 BA1 1,1  couple; dyad; K2; K1,1 2-1
3 3 3-0 0000x0 BCA00B0 0,0,0  three strangers 3-0
3 3 3-1 0010x1 BCA00B1 1,1,0  three's a crowd, Alice out 3-1
3 3 3-2 0100x2 BCA01B0 1,1,0  three's a crowd, Bob out 3-1
3 3 3-3 0110x3 BCA01B1 2,1,1  everybody knows Carol 3-3
3 3 3-4 1000x4 BCA10B0 1,1,0  three's a crowd, Carol out 3-1
3 3 3-5 1010x5 BCA10B1 2,1,1  everybody knows Bob 3-3
3 3 3-6 1100x6 BCA11B0 2,2,1,1TD>  everybody knows Alice 3-3
3 3 3-7 1110x7 BCA11B1 2,2,2  three musketeers; K3; C3 3-7
4 6 4-0 0000000x0 BCDA000B00C0 0,0,0,0  four strangers 4-0
4 6 4-1 0000010x1 BCDA000B00C1 1,1,0,0  couple: Carol & Doug 4-1
4 6 4-2 0000100x2 BCDA000B01C0 1,1,0,0  couple: Bob & Doug 4-1
4 6 4-3 0000110x3 BCDA000B01C1 2,1,1,0  Doug knows Bob and Carol, not Alice 4-3
4 6 4-4 0001000x4 BCDA000B10C0 1,1,0,0  couple: Bob and Carol 4-1
4 6 4-5 0001010x5 BCDA000B10C1 2,1,1,0  Carol knows Bob and Doug, not Alice 4-3
4 6 4-6 0001100x6 BCDA000B11C0 2,1,1,0  Bob knows Carol and Doug, not Alice 4-3
4 6 4-7 0001110x7 BCDA000B11C1 2,2,2,0  triangle; clique with Alice excluded 4-7
4 6 4-8 0010000x8 BCDA001B00C0 1,1,0,0  couple: Alice and Doug 4-1
4 6 4-9 0010010x9 BCDA001B00C1 2,1,1,0  Doug knows Alice and Carol, not Bob 4-3
4 6 4-10 0010100xA BCDA001B01C0 2,1,1,0  Doug knows Alice and Bob, not Carol 4-3
4 6 4-11 0010110xB BCDA001B01C1 3,1,1,1  claw; everybody knows Alice 4-11
4 6 4-12 0011000xC BCDA001B10C0 1,1,1,1  two couples: Bob & Carol, Alice & Doug 4-12
4 6 4-13 0011010xD BCDA001B10C1 2,2,1,1  Carol and Doug are a couple,plus Carol is friends with Bob andDoug is friends with Alice; P4 4-13
4 6 4-14 0011100xE BCDA001B11C0 2,2,1,1  Bob and Doug are a couple,plus Bob is friends with Carol andDoug is friends with Alice; P4 4-13
4 6 4-15 0011110xF BCDA001B11C1 3,2,2,1  kite with Doug -> Alice tail 4-15
4 6 4-16 0100000x10 BCDA010B00C0 1,1,0,0  couple: Alice and Carol 4-1
4 6 4-17 0100010x11 BCDA010B00C1 2,1,1,0  Carol knows Alice and Doug, not Bob 4-3
4 6 4-18 0100100x12 BCDA010B01C0 1,1,1,1  two couples: Alice and Carol, Bob and Doug 4-12
4 6 4-19 0100110x13 BCDA010B01C1 2,2,1,1  Carol and Doug are a couple,plus Carol is friends with Alice andDoug is friends with Bob; P4 4-13
4 6 4-20 0101000x14 BCDA010B10C0 2,1,1,0  Carol knows Alice and Bob, not Doug 4-3
4 6 4-21 0101010x15 BCDA010B10C1 3,1,1,1  claw; everybody knows Carol 4-11
4 6 4-22 0101100x16 BCDA010B11C0 2,2,1,1  Bob and Carol are a couple,plus Bob is friends with Doug andCarol is friends with Alice; P4 4-13
4 6 4-23 0101110x17 BCDA010B11C1 3,2,2,1  kite with Carol -> Alice tail 4-15
4 6 4-24 0110000x18 BCDA011B00C0 2,1,1,0  Alice knows Carol and Doug, not Bob 4-3
4 6 4-25 0110010x19 BCDA011B00C1 2,2,2,0  triangle; clique with Bob excluded 4-7
4 6 4-26 0110100x1A BCDA011B01C0 2,2,1,1  Alice and Doug are a couple,plus Alice is friends with Carol andDoug is friends with Bob; P4 4-13
4 6 4-27 0110110x1B BCDA011B01C1 3,2,2,1  kite with Doug -> Bob tail 4-15
4 6 4-28 0111000x1C BCDA011B10C0 2,2,1,1  Alice and Carol are a couple,plus Alice is friends with Doug andCarol is friends with Bob; P4 4-13
4 6 4-29 0111010x1D BCDA011B10C1 3,2,2,1  kite with Carol -> Bob tail 4-15
4 6 4-30 0111100x1E BCDA011B11C0 2,2,2,2  horizontal bowtie; K2,2; C4 4-30
4 6 4-31 0111110x1F BCDA011B11C1 3,3,2,2  everybody knows everybody except Alice and Bob 4-31
4 6 4-32 1000000x20 BCDA100B00C0 1,1,0,0  couple: Alice and Bob 4-1
4 6 4-33 1000010x21 BCDA100B00C1 1,1,1,1  two couples: Bob & Carol, Alice & Doug 4-12
4 6 4-34 1000100x22 BCDA100B01C0 2,1,1,0  Bob knows Alice and Doug, not Carol 4-3
4 6 4-35 1000110x23 BCDA100B01C1 2,2,1,1  Bob and Doug are a couple,plus Bob is friends with Alice andDoug is friends with Carol; P4 4-13
4 6 4-36 1001000x24 BCDA100B10C0 2,1,1,0  Bob knows Alice and Carol, not Doug 4-3
4 6 4-37 1001010x25 BCDA100B10C1 2,2,1,1  Bob and Carol are a couple,plus Bob is friends with Alice andCarol is friends with Doug; P4 4-13
4 6 4-38 1001100x26 BCDA100B11C0 3,1,1,1  claw; everybody knows Bob 4-11
4 6 4-39 1001110x27 BCDA100B11C1 3,2,2,1  kite with Bob -> Alice tail 4-15
4 6 4-40 1010000x28 BCDA101B00C0 2,1,1,0  Alice knows Bob and Doug, not Carol 4-3
4 6 4-41 1010010x29 BCDA101B00C1 2,2,1,1  Alice and Doug are a couple,plus Alice is friends with Bob andDoug is friends with Carol; P4 4-13
4 6 4-42 1010100x2A BCDA101B01C0 2,2,2,0  triangle; clique with Carol excluded 4-7
4 6 4-43 1010110x2B BCDA101B01C1 3,2,2,1  kite with Doug -> Carol tail 4-15
4 6 4-44 1011000x2C BCDA101B10C0 2,2,1,1  Alice and Doug are a couple,plus Alice is friends with Bob andDoug is friends with Carol; P4 4-13
4 6 4-45 1011010x2D BCDA101B10C1 2,2,2,2  vertical bowtie; K2,2; C4 4-30
4 6 4-46 1011100x2E BCDA101B11C0 3,2,2,1  kite with Bob -> Carol tail 4-15
4 6 4-47 1011110x2F BCDA101B11C1 3,3,2,2  everybody knows everybody except Alice and Carol 4-31
4 6 4-48 1100000x30 BCDA110B00C0 2,1,1,0  Alice knows Bob and Carol, not Doug 4-3
4 6 4-49 1100010x31 BCDA110B00C1 2,2,1,1  Alice and Carol are a couple,plus Alice is friends with Bob andCarol is friends with Doug; P4 4-13
4 6 4-50 1100100x32 BCDA110B01C0 2,2,1,1  Alice and Bob are a couple,plus Alice is friends with Carol andBob is friends with Doug; P4 4-13
4 6 4-51 1100110x33 BCDA110B01C1 2,2,2,2  box; K2,2; C4 4-30
4 6 4-52 1101000x34 BCDA110B10C0 2,2,2,0  triangle; clique with Doug excluded 4-7
4 6 4-53 1101010x35 BCDA110B10C1 3,2,2,1  kite with Carol -> Doug tail 4-15
4 6 4-54 1101100x36 BCDA___B__C_ 3,2,2,1  kite with Bob -> Doug tail 4-15
4 6 4-55 1101110x37 BCDA110B11C1 3,3,2,2  everybody knows everybody except Alice and Doug 4-31
4 6 4-56 1110000x38 BCDA111B00C0 3,1,1,1  claw; everybody knows Alice 4-11
4 6 4-57 1110010x39 BCDA111B00C1 3,2,2,1  kite with Alice -> Bob tail 4-15
4 6 4-58 1110100x3A BCDA111B01C0 3,2,2,1  kite with Alice -> Carol tail 4-15
4 6 4-59 1110110x3B BCDA111B01C1 3,3,2,2  everybody knows everybody except Bob and Carol 4-31
4 6 4-60 1111000x3C BCDA111B10C0 3,2,2,1  kite with Alice -> Doug tail 4-15
4 6 4-61 1111010x3D BCDA111B10C1 3,3,2,2  everybody knows everybody except Bob and Doug 4-31
4 6 4-62 1111100x3E BCDA111B11C0 3,3,2,2  everybody knows everybody except Carol and Doug 4-31
4 6 4-63 1111110x3F BCDA111B11C1 3,3,3,3  K4; W4 4-63

```