Related papers: Random Hyperbolic Graphs: Degree Sequence and Clus…
Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…
Diffusion generative models (DMs) have achieved promising results in image and graph generation. However, real-world graphs, such as social networks, molecular graphs, and traffic graphs, generally share non-Euclidean topologies and hidden…
Hyperbolic models are known to produce networks with properties observed empirically in most network datasets, including heavy-tailed degree distribution, high clustering, and hierarchical structures. As a result, several embeddings…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
Generative network models play an important role in algorithm development, scaling studies, network analysis, and realistic system benchmarks for graph data sets. The commonly used graph-based benchmark model R-MAT has some drawbacks…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
We introduce a model for the randomization of complex networks with geometric structure. The geometric randomization (GR) model assumes a homogeneous distribution of the nodes in an underlying similarity space and uses rewirings of the…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
First principle network models are crucial to make sense of the intricate topology of real complex networks. While modeling efforts have been quite successful in undirected networks, generative models for networks with asymmetric…
In this paper, we present a detailed analysis of the global clustering coefficient in scale-free graphs. Many observed real-world networks of diverse nature have a power-law degree distribution. Moreover, the observed degree distribution…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
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…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
We consider a model for complex networks that was recently proposed as a model for complex networks by Krioukov et al. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are connected if they are at…
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…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
We study the average nearest neighbor degree $a(k)$ of vertices with degree $k$. In many real-world networks with power-law degree distribution $a(k)$ falls off in $k$, a property ascribed to the constraint that any two vertices are…