Four Colours vs GraphWeave

Could be a map of USA or your country colored using four colors in such a way that Nebraska and Missouri (as well as any two contiguous regions or states) wouldn’t be filled with one color? It turns out that you can manage to do it with any map. And this seems to be the first statement in science proved with computer aid. You can verify this statement for variety of maps, study up geography and visit Martin Gardner country by the way. Maps in this release: • Commonwealth of Australia, • Republic of Austria, • French Republic, • Federal Republic of Germany, • United Mexican States, • Republic of Poland, • Portuguese Republic, • Kingdom of Spain, • Kingdom of Sweden, • Swiss Confederation, • United States of America, • United Kingdom of Great Britain and Northern Ireland.

GraphWeave lets you draw a network by hand and instantly see its geometric and structural properties, computed on the spot and shown in color. Place nodes and links with your finger, and discrete curvature and centrality measures appear right away. ■ Features • Sketch nodes and links directly; drag to arrange them freely • Discrete Ollivier–Ricci curvature for every link • Six node measures: degree, closeness, betweenness and eigenvector centrality, clustering coefficient, and PageRank • Links or nodes are automatically colored on a coolwarm (blue→red) scale, with numeric labels • Save graphs on your device and reopen them anytime to re-analyze • Works fully offline — no account, no network connection ■ Who it's for • Students and teachers learning graph theory and network science • Anyone who wants a hands-on feel for curvature and centrality • Researchers who need a quick look at the structure of a small network ■ Privacy GraphWeave collects no data. Your graphs are stored only on your device and are never sent anywhere. No ads. Metric definitions follow the open-source networkx implementations.