11 problems

Consider real-world networks whose degree distribution follows a power law, and let PageRank be the centrality measure assigned to their vertices. Power-law hypothesis. The PageRan…

Consider the two-colored PAM with $m_1=m_2=m$, attachment kernel … and minority-vertex probability $\mu_1$. PageRank fairness conjecture. For every sufficiently small $c>0$, there…

Scale-free infinity-PageRank conjecture. If $d_i\sim X$ where $X$ is a regularly varying random variable, then $PR_\infty(i)$ will also be scale-free.

μ-PageRank monotonicity and range conjecture. The function $([?])_i$ is monotonic for all $i$ and

Range-shrinking conjecture. The range of values of $[?]$-PageRank shrinks as $[?]\to\infty$.

Monotonicity conjecture. The function $([?])_i$ is monotonic for every node $i$.

Let $G$ be any unweighted directed graph, possibly with loops and bidirected arcs, and let $\alpha_1$ and $\alpha_2$ be two jumping constants. For each jumping constant, write…

Uniqueness conjecture. The multilinear PageRank vector should be unique whenever $\alpha<1$.

Let $G$ be a directed graph with $d_{min}^{out}>0$. For a parameter $\alpha$ and associated PageRank random walk, let $\mathbf{R}$ be the probability transition matrix, given by ……

PageRank-order convergence conjecture. In the limit

Let $\mathcal{E}_\mathrm{in}(\mathcal{I})\neq\emptyset$ and $\mathcal{E}_{\overline{\mathcal{I}}}$ be given. Let $\mathcal{E}_{\mathcal{I}}$ and…