Turn a Fiedler ordering into an actual cutThe graph carries a highlighted set of nodes. Crossing edges are orange. In the numerical placement each node’s horizontal position is its Fiedler-vector value. Equal values are stacked vertically for legibility, without changing their horizontal position. A dashed threshold selects every node to its left. The initial threshold sits in the first gap and selects nodes 7 and 8, with four crossing edges, a smaller side of two nodes, and cut score four divided by two, which is two. Values suggest an order; a cut picks a side Orange edges cross the chosen boundary. 1 2 3 4 5 6 7 8 Horizontal position = Fiedler value Choose every node left of the line. 1 2 3 4 5 6 7 8 −0.425 −0.263 0.263 0.425 0 Equal values stay together when we move the threshold.
Turn a Fiedler ordering into an actual cutThe graph carries a highlighted set of nodes. Crossing edges are orange. In the numerical placement each node’s horizontal position is its Fiedler-vector value. Equal values are stacked vertically for legibility, without changing their horizontal position. A dashed threshold selects every node to its left. The initial threshold sits in the first gap and selects nodes 7 and 8, with four crossing edges, a smaller side of two nodes, and cut score four divided by two, which is two. Values give an order. A cut chooses a side. Orange edges cross the chosen boundary. 1 2 3 4 5 6 7 8 Horizontal position = Fiedler value Choose every node left of the line. 1 2 3 4 5 6 7 8 −0.425 −0.263 0.263 0.425 0 Equal-valued nodes stay together.

Choose one of the three gaps. Nodes below the threshold form the blue group; orange edges cross to the other group. The wiring and node values stay fixed. The threshold readout is rounded.

≈ −0.34
Crossing edges4
Smaller side2
Cut score2.000

Selected nodes: 7, 8.

Horizontal position shows each node’s Fiedler value. Nodes below the dashed threshold form the selected group. Equal values are stacked vertically for readability and always stay on the same side of the threshold.