8 problems

Jordan lower-tail transition conjecture. The lower tail of the Jordan-$2$ ordering undergoes a transition from polynomial decay to stretched-exponential decay, and a similar phenom…

Central-vertex proportion conjecture. As $K\to\infty$, this proportion converges to

Let $A$ be the Hopf algebra under consideration, let $a\in A$, and let $W$ be a sum of words in the image of the functor $F$ from tangles to the relevant algebraic structure. Algeb…

Let $K_n$ denote the complete graph on $n$ vertices, and call a network asymptotically pairwise stable if it satisfies asymptotic pairwise stability for the eigenvector-centrality…

Let an asymptotically pairwise stable network (APSN) be a network satisfying asymptotic pairwise stability for the relevant centrality game, and let $\emptyset_n$ and $K_n$ denote…

Uniform edge betweenness centrality conjecture. Each of these seven classes of circulant graphs has uniform edge betweenness centrality but is not edge-transitive.

Let $P_n^k$ denote the $k$th power of the path graph on $n$ vertices, and let … be the Cartesian product of $m$ copies of $P_n^k$, with $n\geq 4k+1$. The leverage-centrality count…

Let a preferential attachment tree grow by attaching new vertices to existing vertices with probability proportional to a function $f$ of the vertex degree. A vertex is a persisten…