相关论文: Scalable Generation of Scale-free Graphs

Big graphs (networks) arising in numerous application areas pose significant challenges for graph analysts as these graphs grow to billions of nodes and edges and are prohibitively large to fit in the main memory. Finding the number of…

The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…

Over recent years, denoising diffusion generative models have come to be considered as state-of-the-art methods for synthetic data generation, especially in the case of generating images. These approaches have also proved successful in…

We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…

AT-free graphs are characterized by vertex elimination orders. We show that these AT-free orders of a graph can be generated in constant amortized time.

Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which…

Classical graph modeling approaches such as Erd\H{o}s R\'{e}nyi (ER) random graphs or Barab\'asi-Albert (BA) graphs, here referred to as stylized models, aim to reproduce properties of real-world graphs in an interpretable way. While…

Graph foundation models have demonstrated remarkable adaptability across diverse downstream tasks through large-scale pretraining on graphs. However, existing implementations of the backbone model, graph transformers, are typically limited…

Finding maximum-weight independent sets in graphs is an important NP-hard optimization problem. Given a vertex-weighted graph $G$, the task is to find a subset of pairwise non-adjacent vertices of $G$ with maximum weight. Most recently…

The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice $\mathbb{Z}^d$, $d\ge1$, because it fulfills several stylized facts observed in large…

Graph generation is an important area in network science. Traditional approaches focus on replicating specific properties of real-world graphs, such as small diameters or power-law degree distributions. Recent advancements in deep learning,…

Geometric scale-free random graphs are popular models for networks that exhibit as heavy-tailed degree distributions, small-worldness and high clustering. In these models, vertices have weights that cause the heavy-tailed degrees and are…

Recently we create so much data (2.5 quintillion bytes every day) that 90% of the data in the world today has been created in the last two years alone [1]. This data comes from sensors used to gather traffic or climate information, posts to…

Graph generative models become increasingly effective for data distribution approximation and data augmentation. While they have aroused public concerns about their malicious misuses or misinformation broadcasts, just as what Deepfake…

Based on earlier work on regular quantum graphs we show that a large class of scaling quantum graphs with arbitrary topology are explicitly analytically solvable. This is surprising since quantum graphs are excellent models of quantum chaos…

We propose a framework using normalizing-flow based models, SELF-Referencing Embedded Strings, and multi-objective optimization that efficiently generates small molecules. With an initial training set of only 100 small molecules, FastFlows…

We define a growing model of random graphs. Given a sequence of nonnegative integers $\{d_n\}_{n=0}^\infty$ with the property that $d_i\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\ldots$ by the…

The structural properties of naturally arising social graphs are extensively studied to understand their evolution. Prior approaches for modeling network dynamics typically rely on rule-based models, which lack realism and generalizability,…

We study the problem of point-to-point distance querying for massive scale-free graphs, which is important for numerous applications. Given a directed or undirected graph, we propose to build an index for answering such queries based on a…

A construction of Alon yields a sequence of highly pseudorandom triangle-free graphs with edge density significantly higher than one might expect from comparison with random graphs. We give an alternative construction for such graphs.