Related papers: Geometric Graph Properties of the Spatial Preferre…
Global degree/strength based preferential attachment is widely used as an evolution mechanism of networks. But it is hard to believe that any individual can get global information and shape the network architecture based on it. In this…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination…
A random k-out mapping (digraph) on [n] is generated by choosing k random images of each vertex one at a time, subject to a "preferential attachment" rule: the current vertex selects an image i with probability proportional to a given…
From longitudinal biomedical studies to social networks, graphs have emerged as a powerful framework for describing evolving interactions between agents in complex systems. In such studies, after pre-processing, the data can be represented…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
Complex networks represented as node adjacency matrices constrains the application of machine learning and parallel algorithms. To address this limitation, network embedding (i.e., graph representation) has been intensively studied to learn…
Theta-graphs are a type of spatial graph with two vertices connected by three edges. We investigate embeddings of theta-graphs in the square and simple cubic lattices, using a combination of the Wang-Landau Monte Carlo method with a variant…
Evaluating similarity between graphs is of major importance in several computer vision and pattern recognition problems, where graph representations are often used to model objects or interactions between elements. The choice of a distance…
A temporal network -- a collection of snapshots recording the evolution of a network whose links appear and disappear dynamically -- can be interpreted as a trajectory in graph space. In order to characterize the complex dynamics of such…
The generalized distance matrix of a graph is the matrix whose entries depend only on the pairwise distances between vertices, and the generalized distance spectrum is the set of eigenvalues of this matrix. This framework generalizes many…
For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
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…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
Motivated by widely observed examples in nature, society and software, where groups of already related nodes arrive together and attach to an existing network, we consider network growth via sequential attachment of linked node groups, or…
Real-world social networks often exhibit high levels of clustering, positive degree assortativity, short average path lengths (small-world property) and right-skewed but rarely power law degree distributions. On the other hand homophily,…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…