Zobrazeno 1 - 10
of 312
pro vyhledávání: '"Pralat, Pawel"'
We present two ways to measure the simplicial nature of a hypergraph: the simplicial ratio and the simplicial matrix. We show that the simplicial ratio captures the frequency, as well as the rarity, of simplicial interactions in a hypergraph while th
Externí odkaz:
http://arxiv.org/abs/2408.11806
In this paper, we propose a scalable community detection algorithm using hypergraph modularity function, h-Louvain. It is an adaptation of the classical Louvain algorithm in the context of hypergraphs. We observe that a direct application of the Louv
Externí odkaz:
http://arxiv.org/abs/2406.17556
Let $\mathcal{T}$ be a Galton-Watson tree with a given offspring distribution $\xi$, where $\xi$ is a $Z_{\geq 0}$-valued random variable with $E[\xi] = 1$ and $0 < \sigma^{2}:=Var[\xi] < \infty$. For $n \geq 1$, let $T_{n}$ be the tree $\mathcal{T}$
Externí odkaz:
http://arxiv.org/abs/2404.01545
We study the 2-offer semirandom 3-uniform hypergraph model on $n$ vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3. We show a strategy that constructs a perfect
Externí odkaz:
http://arxiv.org/abs/2401.00559
The Artificial Benchmark for Community Detection (ABCD) graph is a random graph model with community structure and power-law distribution for both degrees and community sizes. The model generates graphs similar to the well-known LFR model but it is f
Externí odkaz:
http://arxiv.org/abs/2312.00238
Autor:
Eide, Austin, Prałat, Paweł
We investigate the linear chromatic number $\chi_{\text{lin}}(G(n,p))$ of the binomial random graph $G(n,p)$ on $n$ vertices in which each edge appears independently with probability $p=p(n)$. For dense random graphs ($np \to \infty$ as $n \to \infty
Externí odkaz:
http://arxiv.org/abs/2311.08560
The semi-random graph process is an adaptive random graph process in which an online algorithm is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the algorithm independently and uniformly at random. The
Externí odkaz:
http://arxiv.org/abs/2311.05533
This paper shows how information about the network's community structure can be used to define node features with high predictive power for classification tasks. To do so, we define a family of community-aware node features and investigate their prop
Externí odkaz:
http://arxiv.org/abs/2311.04730
Autor:
Mohan, Divyarthi, Pralat, Pawel
We study information aggregation in networks when agents interact to learn a binary state of the world. Initially each agent privately observes an independent signal which is "correct" with probability $\frac{1}{2}+\delta$ for some $\delta > 0$. At e
Externí odkaz:
http://arxiv.org/abs/2309.04691
We investigate a combinatorial optimization problem that involves patrolling the edges of an acute triangle using a unit-speed agent. The goal is to minimize the maximum (1-gap) idle time of any edge, which is defined as the time gap between consecut
Externí odkaz:
http://arxiv.org/abs/2307.13153