Back to the portfolio

A small note on the design

What’s with
the graph.

From a graph to a tree

A weighted graph is a set of vertices connected by edges, with a numerical weight attached to each edge. These weights need not match the geometric lengths in a drawing. [1]

For a finite, connected, undirected graph, a spanning tree connects every vertex and contains no cycles. With n vertices, it has n − 1 edges. [2] A minimum spanning tree (MST) minimizes the total edge weight among all spanning trees of a weighted graph. [1]

In the portfolio

The portfolio starts with a dense weighted graph. As you scroll, reverse-delete considers edges from heaviest to lightest, removing an edge only when the graph remains connected. Every vertex stays; the surviving connections form an MST. [2]

I chose this concept to represent finding essential structure inside complexity. It preserves the relationships needed to keep the whole connected, giving a concrete form to the theme:

Understand complexity.
Build clarity.

The portfolio’s weighted graphThe same 25 square vertices appear in both views. The control switches between the full graph’s 192 edges and its minimum spanning tree’s 24 edges. Numbers show selected edge weights.123456
25 vertices / 192 edges25 vertices / 24 edges / MST

Same vertices. Essential connections.

References

  1. R. C. Prim (1957). Shortest Connection Networks and Some Generalizations. Bell System Technical Journal, 36(6), 1389–1401. Minimum-length formulation: p. 1389; weighted-graph model and generalization: pp. 1395–1396.
  2. J. B. Kruskal, Jr. (1956). On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem. Proceedings of the American Mathematical Society, 7(1), 48–50. Spanning-tree equivalences: pp. 49–50; reverse-delete: Construction A′, p. 49.
Back to the portfolio