Incorporating structural features into random-graph calculations should bring theoretical models describing the properties and behaviour of complex networks closer to real-world systems. You have full ...

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2024. Many real-world networks change dynamically but can be notoriously ...

Abstract: Random graph models are commonly used as a null-hypothesis in the study of real-world networks. It is important that these networks resemble the real network under study, since they are used ...

The classical result of Erdos and Renyi shows that the random graph G(n,p) experiences sharp phase transition around p=1/n – for any ε0 and p=(1-ε)/n, all connected components of G(n,p) are typically ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

Venture capital firms use a variety of accumulated resources to inform their investment activities, but do the rely solely on their own resources or do they employ other firms' resources to complement ...

Abstract: Random walks on graphs have wide-ranging applications, including target node search on graphs and structural exploration of graphs. In recent years, analyses have been conducted not only on ...