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Random graphs with prescribed degree sequences have been widely used as a model of complex networks. Comparing an observed network to an ensemble of such graphs allows one to detect deviations from randomness in network properties. Here we…
Sampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. An important requirement is that the…
The ability of a peer-to-peer (P2P) system to effectively host decentralized applications often relies on the availability of a peer-sampling service, which provides each participant with a random sample of other peers. Despite the…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
Graph neural networks have shown superior performance in a wide range of applications providing a powerful representation of graph-structured data. Recent works show that the representation can be further improved by auxiliary tasks.…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…
We study the random graph obtained by random deletion of vertices or edges from a random graph with given vertex degrees. A simple trick of exploding vertices instead of deleting them, enables us to derive results from known results for…
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
We consider the following common network analysis problem: given a degree sequence $\mathbf{d} = (d_1, \dots, d_n) \in \mathbb N^n$ return a uniform sample from the ensemble of all simple graphs with matching degrees. In practice, the…
In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the…
In this note we give sufficient conditions for the convergence of the iterative algorithm called weighted-average consensus in directed graphs. We study the discrete-time form of this algorithm. We use standard techniques from matrix theory…
Graph sampling via crawling has become increasingly popular and important in the study of measuring various characteristics of large scale complex networks. While powerful, it is known to be challenging when the graph is loosely connected…
Let $F$ be a probability distribution with support on the non-negative integers. Four methods for generating a simple undirected graph with (approximate) degree distribution $F$ are described and compared. Two methods are based on the so…
Exploring small connected and induced subgraph patterns (CIS patterns, or graphlets) has recently attracted considerable attention. Despite recent efforts on computing the number of instances a specific graphlet appears in a large graph…
Graph representation learning has made major strides over the past decade. However, in many relational domains, the input data are not suited for simple graph representations as the relationships between entities go beyond pairwise…
Network embedding techniques inspired by word2vec represent an effective unsupervised relational learning model. Commonly, by means of a Skip-Gram procedure, these techniques learn low dimensional vector representations of the nodes in a…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…