Related papers: Network Representation Using Graph Root Distributi…
Graph randomization techniques play a crucial role in network analysis, allowing researchers to assess the statistical significance of observed network properties and distinguish meaningful patterns from random fluctuations. In this survey…
Streets networks provide an invaluable source of information about the different temporal and spatial patterns emerging in our cities. These streets are often represented as graphs where intersections are modelled as nodes and streets as…
Data in the form of graphs, or networks, arise naturally in a number of contexts; examples include social networks and biological networks. We are often faced with the availability of multiple graphs on a single set of nodes. In this…
Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively…
In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…
The graph structure is a commonly used data storage mode, and it turns out that the low-dimensional embedded representation of nodes in the graph is extremely useful in various typical tasks, such as node classification, link prediction ,…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
Graph neural networks (GNNs) emerge as a powerful family of representation learning models on graphs. To derive node representations, they utilize a global model that recursively aggregates information from the neighboring nodes. However,…
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…
We introduce two new bootstraps for exchangeable random graphs. One, the "empirical graphon bootstrap", is based purely on resampling, while the other, the "histogram bootstrap", is a model-based "sieve" bootstrap. We show that both of them…
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is…
We study the independence structure of finitely exchangeable distributions over random vectors and random networks. In particular, we provide necessary and sufficient conditions for an exchangeable vector so that its elements are completely…
Given a valued graph, where both the nodes and the edges of the graph are associated with one or several values, any network function for a given node must be defined in terms of that node and its connected nodes in the graph. Generally,…