Geist Demo for SciPy 2024

Suppose we have a Hamming numbers (let's call it a Fish Graph) dataset stored in DuckDB, which contains a table named edges. The fish dataset was generated based on the following rules:

The initial starting node is 1.

The edge can be either 2 or 3 or 5.

Start node times edge equals to the end node.

Below shows the first 5 rows of the fish table:

startnode	label	endnode
1	3	3
1	2	2
1	5	5
5	3	15
2	3	6

1. Visualization of the Fish Graph

        graph LR
	style N1 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N2 fill:#b3e2cd, stroke:#333, stroke-width:1px
N1(1) --> |× 2| N2(2)
	style N3 fill:#b3e2cd, stroke:#333, stroke-width:1px
N1 --> |× 3| N3(3)
	style N4 fill:#b3e2cd, stroke:#333, stroke-width:1px
N1 --> |× 5| N4(5)
	style N5 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N6 fill:#b3e2cd, stroke:#333, stroke-width:1px
N5(10) --> |× 2| N6(20)
	style N7 fill:#b3e2cd, stroke:#333, stroke-width:1px
N5 --> |× 3| N7(30)
	style N8 fill:#b3e2cd, stroke:#333, stroke-width:1px
N5 --> |× 5| N8(50)
	style N9 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N10 fill:#b3e2cd, stroke:#333, stroke-width:1px
N9(100) --> |× 2| N10(200)
	style N11 fill:#b3e2cd, stroke:#333, stroke-width:1px
N9 --> |× 3| N11(300)
	style N12 fill:#b3e2cd, stroke:#333, stroke-width:1px
N9 --> |× 5| N12(500)
	style N13 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N14 fill:#b3e2cd, stroke:#333, stroke-width:1px
N13(108) --> |× 2| N14(216)
	style N15 fill:#b3e2cd, stroke:#333, stroke-width:1px
N13 --> |× 3| N15(324)
	style N16 fill:#b3e2cd, stroke:#333, stroke-width:1px
N13 --> |× 5| N16(540)
	style N17 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N18 fill:#b3e2cd, stroke:#333, stroke-width:1px
N17(12) --> |× 2| N18(24)
	style N19 fill:#b3e2cd, stroke:#333, stroke-width:1px
N17 --> |× 3| N19(36)
	style N20 fill:#b3e2cd, stroke:#333, stroke-width:1px
N17 --> |× 5| N20(60)
	style N21 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N22 fill:#b3e2cd, stroke:#333, stroke-width:1px
N21(120) --> |× 2| N22(240)
	style N23 fill:#b3e2cd, stroke:#333, stroke-width:1px
N21 --> |× 3| N23(360)
	style N24 fill:#b3e2cd, stroke:#333, stroke-width:1px
N21 --> |× 5| N24(600)
	style N25 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N26 fill:#b3e2cd, stroke:#333, stroke-width:1px
N25(125) --> |× 2| N26(250)
	style N27 fill:#b3e2cd, stroke:#333, stroke-width:1px
N25 --> |× 3| N27(375)
	style N28 fill:#b3e2cd, stroke:#333, stroke-width:1px
N25 --> |× 5| N28(625)
	style N29 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N30 fill:#b3e2cd, stroke:#333, stroke-width:1px
N29(128) --> |× 2| N30(256)
	style N31 fill:#b3e2cd, stroke:#333, stroke-width:1px
N29 --> |× 3| N31(384)
	style N32 fill:#b3e2cd, stroke:#333, stroke-width:1px
N29 --> |× 5| N32(640)
	style N33 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N34 fill:#b3e2cd, stroke:#333, stroke-width:1px
N33(135) --> |× 2| N34(270)
	style N35 fill:#b3e2cd, stroke:#333, stroke-width:1px
N33 --> |× 3| N35(405)
	style N36 fill:#b3e2cd, stroke:#333, stroke-width:1px
N33 --> |× 5| N36(675)
	style N37 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N38 fill:#b3e2cd, stroke:#333, stroke-width:1px
N37(144) --> |× 2| N38(288)
	style N39 fill:#b3e2cd, stroke:#333, stroke-width:1px
N37 --> |× 3| N39(432)
	style N40 fill:#b3e2cd, stroke:#333, stroke-width:1px
N37 --> |× 5| N40(720)
	style N41 fill:#b3e2cd, stroke:#333, stroke-width:1px
N41(15) --> |× 2| N7
	style N42 fill:#b3e2cd, stroke:#333, stroke-width:1px
N41 --> |× 3| N42(45)
	style N43 fill:#b3e2cd, stroke:#333, stroke-width:1px
N41 --> |× 5| N43(75)
	style N44 fill:#b3e2cd, stroke:#333, stroke-width:1px
N44(150) --> |× 2| N11
	style N45 fill:#b3e2cd, stroke:#333, stroke-width:1px
N44 --> |× 3| N45(450)
	style N46 fill:#b3e2cd, stroke:#333, stroke-width:1px
N44 --> |× 5| N46(750)
	style N47 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N48 fill:#b3e2cd, stroke:#333, stroke-width:1px
N47(16) --> |× 2| N48(32)
	style N49 fill:#b3e2cd, stroke:#333, stroke-width:1px
N47 --> |× 3| N49(48)
	style N50 fill:#b3e2cd, stroke:#333, stroke-width:1px
N47 --> |× 5| N50(80)
	style N51 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N52 fill:#b3e2cd, stroke:#333, stroke-width:1px
N51(160) --> |× 2| N52(320)
	style N53 fill:#b3e2cd, stroke:#333, stroke-width:1px
N51 --> |× 3| N53(480)
	style N54 fill:#b3e2cd, stroke:#333, stroke-width:1px
N51 --> |× 5| N54(800)
	style N55 fill:#b3e2cd, stroke:#333, stroke-width:1px
N55(162) --> |× 2| N15
	style N56 fill:#b3e2cd, stroke:#333, stroke-width:1px
N55 --> |× 3| N56(486)
	style N57 fill:#b3e2cd, stroke:#333, stroke-width:1px
N55 --> |× 5| N57(810)
	style N58 fill:#b3e2cd, stroke:#333, stroke-width:1px
N58(18) --> |× 2| N19
	style N59 fill:#b3e2cd, stroke:#333, stroke-width:1px
N58 --> |× 3| N59(54)
	style N60 fill:#b3e2cd, stroke:#333, stroke-width:1px
N58 --> |× 5| N60(90)
	style N61 fill:#b3e2cd, stroke:#333, stroke-width:1px
N61(180) --> |× 2| N23
N61 --> |× 3| N16
	style N62 fill:#b3e2cd, stroke:#333, stroke-width:1px
N61 --> |× 5| N62(900)
	style N63 fill:#b3e2cd, stroke:#333, stroke-width:1px
N63(192) --> |× 2| N31
	style N64 fill:#b3e2cd, stroke:#333, stroke-width:1px
N63 --> |× 3| N64(576)
	style N65 fill:#b3e2cd, stroke:#333, stroke-width:1px
N63 --> |× 5| N65(960)
	style N66 fill:#b3e2cd, stroke:#333, stroke-width:1px
N2 --> |× 2| N66(4)
	style N67 fill:#b3e2cd, stroke:#333, stroke-width:1px
N2 --> |× 3| N67(6)
N2 --> |× 5| N5
	style N68 fill:#b3e2cd, stroke:#333, stroke-width:1px
N6 --> |× 2| N68(40)
N6 --> |× 3| N20
N6 --> |× 5| N9
	style N69 fill:#b3e2cd, stroke:#333, stroke-width:1px
N10 --> |× 2| N69(400)
N10 --> |× 3| N24
	style N70 fill:#b3e2cd, stroke:#333, stroke-width:1px
N10 --> |× 5| N70(1000)
N14 --> |× 2| N39
	style N71 fill:#b3e2cd, stroke:#333, stroke-width:1px
N14 --> |× 3| N71(648)
	style N72 fill:#b3e2cd, stroke:#333, stroke-width:1px
N72(225) --> |× 2| N45
N72 --> |× 3| N36
N18 --> |× 2| N49
	style N73 fill:#b3e2cd, stroke:#333, stroke-width:1px
N18 --> |× 3| N73(72)
N18 --> |× 5| N21
N22 --> |× 2| N53
N22 --> |× 3| N40
	style N74 fill:#b3e2cd, stroke:#333, stroke-width:1px
N74(243) --> |× 2| N56
	style N75 fill:#b3e2cd, stroke:#333, stroke-width:1px
N74 --> |× 3| N75(729)
	style N76 fill:#b3e2cd, stroke:#333, stroke-width:1px
N76(25) --> |× 2| N8
N76 --> |× 3| N43
N76 --> |× 5| N25
N26 --> |× 2| N12
N26 --> |× 3| N46
	style N77 fill:#b3e2cd, stroke:#333, stroke-width:1px
N30 --> |× 2| N77(512)
	style N78 fill:#b3e2cd, stroke:#333, stroke-width:1px
N30 --> |× 3| N78(768)
	style N79 fill:#b3e2cd, stroke:#333, stroke-width:1px
N79(27) --> |× 2| N59
	style N80 fill:#b3e2cd, stroke:#333, stroke-width:1px
N79 --> |× 3| N80(81)
N79 --> |× 5| N33
N34 --> |× 2| N16
N34 --> |× 3| N57
N38 --> |× 2| N64
	style N81 fill:#b3e2cd, stroke:#333, stroke-width:1px
N38 --> |× 3| N81(864)
N3 --> |× 2| N67
	style N82 fill:#b3e2cd, stroke:#333, stroke-width:1px
N3 --> |× 3| N82(9)
N3 --> |× 5| N41
N7 --> |× 2| N20
N7 --> |× 3| N60
N7 --> |× 5| N44
N11 --> |× 2| N24
N11 --> |× 3| N62
	style N83 fill:#b3e2cd, stroke:#333, stroke-width:1px
N48 --> |× 2| N83(64)
	style N84 fill:#b3e2cd, stroke:#333, stroke-width:1px
N48 --> |× 3| N84(96)
N48 --> |× 5| N51
N52 --> |× 2| N32
N52 --> |× 3| N65
N15 --> |× 2| N71
	style N85 fill:#b3e2cd, stroke:#333, stroke-width:1px
N15 --> |× 3| N85(972)
N19 --> |× 2| N73
N19 --> |× 3| N13
N19 --> |× 5| N61
N23 --> |× 2| N40
N27 --> |× 2| N46
N31 --> |× 2| N78
	style N86 fill:#b3e2cd, stroke:#333, stroke-width:1px
N66 --> |× 2| N86(8)
N66 --> |× 3| N17
N66 --> |× 5| N6
N68 --> |× 2| N50
N68 --> |× 3| N21
N68 --> |× 5| N10
N69 --> |× 2| N54
N35 --> |× 2| N57
N39 --> |× 2| N81
N42 --> |× 2| N60
N42 --> |× 3| N33
N42 --> |× 5| N72
N45 --> |× 2| N62
N49 --> |× 2| N84
N49 --> |× 3| N37
N49 --> |× 5| N22
N53 --> |× 2| N65
N56 --> |× 2| N85
N4 --> |× 2| N5
N4 --> |× 3| N41
N4 --> |× 5| N76
N8 --> |× 2| N9
N8 --> |× 3| N44
N8 --> |× 5| N26
N12 --> |× 2| N70
N59 --> |× 2| N13
N59 --> |× 3| N55
N59 --> |× 5| N34
N67 --> |× 2| N17
N67 --> |× 3| N58
N67 --> |× 5| N7
N20 --> |× 2| N21
N20 --> |× 3| N61
N20 --> |× 5| N11
N83 --> |× 2| N29
N83 --> |× 3| N63
N83 --> |× 5| N52
N73 --> |× 2| N37
N73 --> |× 3| N14
N73 --> |× 5| N23
N43 --> |× 2| N44
N43 --> |× 3| N72
N43 --> |× 5| N27
N86 --> |× 2| N47
N86 --> |× 3| N18
N86 --> |× 5| N68
N50 --> |× 2| N51
N50 --> |× 3| N22
N50 --> |× 5| N69
N80 --> |× 2| N55
N80 --> |× 3| N74
N80 --> |× 5| N35
N82 --> |× 2| N58
N82 --> |× 3| N79
N82 --> |× 5| N42
N60 --> |× 2| N61
N60 --> |× 3| N34
N60 --> |× 5| N45
N84 --> |× 2| N63
N84 --> |× 3| N38
N84 --> |× 5| N53

2. Visualization of the subgraph extracted from the Fish Graph

Find all nodes that can be reached from node 5 by following either edge 2 or 3.

        graph LR
	style N1 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N2 fill:#b3e2cd, stroke:#333, stroke-width:1px
N1(10) --> |× 2| N2(20)
	style N3 fill:#b3e2cd, stroke:#333, stroke-width:1px
N1 --> |× 3| N3(30)
	style N4 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N5 fill:#b3e2cd, stroke:#333, stroke-width:1px
N4(120) --> |× 2| N5(240)
	style N6 fill:#b3e2cd, stroke:#333, stroke-width:1px
N4 --> |× 3| N6(360)
	style N7 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N8 fill:#b3e2cd, stroke:#333, stroke-width:1px
N7(135) --> |× 2| N8(270)
	style N9 fill:#b3e2cd, stroke:#333, stroke-width:1px
N7 --> |× 3| N9(405)
	style N10 fill:#b3e2cd, stroke:#333, stroke-width:1px
N10(15) --> |× 2| N3
	style N11 fill:#b3e2cd, stroke:#333, stroke-width:1px
N10 --> |× 3| N11(45)
	style N12 fill:#b3e2cd, stroke:#333, stroke-width:1px
	style N13 fill:#b3e2cd, stroke:#333, stroke-width:1px
N12(160) --> |× 2| N13(320)
	style N14 fill:#b3e2cd, stroke:#333, stroke-width:1px
N12 --> |× 3| N14(480)
	style N15 fill:#b3e2cd, stroke:#333, stroke-width:1px
N15(180) --> |× 2| N6
	style N16 fill:#b3e2cd, stroke:#333, stroke-width:1px
N15 --> |× 3| N16(540)
	style N17 fill:#b3e2cd, stroke:#333, stroke-width:1px
N2 --> |× 2| N17(40)
	style N18 fill:#b3e2cd, stroke:#333, stroke-width:1px
N2 --> |× 3| N18(60)
N5 --> |× 2| N14
	style N19 fill:#b3e2cd, stroke:#333, stroke-width:1px
N5 --> |× 3| N19(720)
N8 --> |× 2| N16
	style N20 fill:#b3e2cd, stroke:#333, stroke-width:1px
N8 --> |× 3| N20(810)
N3 --> |× 2| N18
	style N21 fill:#b3e2cd, stroke:#333, stroke-width:1px
N3 --> |× 3| N21(90)
	style N22 fill:#b3e2cd, stroke:#333, stroke-width:1px
N13 --> |× 2| N22(640)
	style N23 fill:#b3e2cd, stroke:#333, stroke-width:1px
N13 --> |× 3| N23(960)
	style N24 fill:#b3e2cd, stroke:#333, stroke-width:1px
N17 --> |× 2| N24(80)
N17 --> |× 3| N4
N11 --> |× 2| N21
N11 --> |× 3| N7
	style N25 fill:#b3e2cd, stroke:#333, stroke-width:1px
N25(5) --> |× 2| N1
N25 --> |× 3| N10
N18 --> |× 2| N4
N18 --> |× 3| N15
N24 --> |× 2| N12
N24 --> |× 3| N5
N21 --> |× 2| N15
N21 --> |× 3| N8