Simplicial complexes generalise graphs to higher dimensions by assembling vertices, edges, triangles and their higher-dimensional analogues into a combinatorial structure that encodes topology and ...

Six years ago, Afonso Bandeira and Shuyang Ling were attempting to come up with a better way to discern clusters in enormous data sets when they stumbled into a surreal world. Ling realized that the ...

The spectral characteristics of graphs and matrices form a central pillar of modern mathematical physics and network theory. At its core, the adjacency matrix of a graph encodes connectivity by ...

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. It started with a bet. In the late 1980s, at a ...