Related papers: Recovering the Structure of Random Linear Graphs
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph…
Given a graph, we associate each edge with the transposition which exchanges the endvertices. Fixing a linear order on the edge set, we obtain a permutation of the vertices. D\'enes proved that the permutation is a full cyclic permutation…
Vertex bisection is a graph partitioning problem in which the aim is to find a partition into two equal parts that minimizes the number of vertices in one partition set that have a neighbor in the other set. We are interested in giving…
It has been recently proposed that the natural connectivity can be used to characterize efficiently the robustness of complex networks. The natural connectivity quantifies the redundancy of alternative routes in the network by evaluating…
Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…
A graph embedding is a representation of graph vertices in a low-dimensional space, which approximately preserves properties such as distances between nodes. Vertex sequence-based embedding procedures use features extracted from linear…
Learning distributed representations for nodes in graphs is a crucial primitive in network analysis with a wide spectrum of applications. Linear graph embedding methods learn such representations by optimizing the likelihood of both…
The recovery of network structure from experimental data is a basic and fundamental problem. Unfortunately, experimental data often do not directly reveal structure due to inherent limitations such as imprecision in timing or other…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…
This work studies fundamental limits for recovering the underlying correspondence among multiple correlated graphs. In the setting of inhomogeneous random graphs, we present and analyze a matching algorithm: first partially match the graphs…
Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance…
Given a hereditary graph property $\mathcal{P}$, consider distributions of random orderings of vertices of graphs $G\in\mathcal{P}$ that are preserved under isomorphisms and under taking induced subgraphs. We show that for many properties…
The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…
We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…
We consider a random graph G(n,p) whose vertex set V has been randomly embedded in the unit square and whose edges are given weight equal to the geometric distance between their end vertices. Then each pair {u,v} of vertices have a distance…
We introduce a graph-theoretic vertex dissolution model that applies to a number of redistribution scenarios such as gerrymandering in political districting or work balancing in an online situation. The central aspect of our model is the…
This paper studies the problem of recovering a hidden vertex correspondence between two correlated graphs when both edge weights and node features are observed. While most existing work on graph alignment relies primarily on edge…
We find the asymptotic number of connected graphs with $k$ vertices and $k-1+l$ edges when $k,l$ approach infinity, reproving a result of Bender, Canfield and McKay. We use the {\em probabilistic method}, analyzing breadth-first search on…
We study the problem of inferring network topology from information cascades, in which the amount of time taken for information to diffuse across an edge in the network follows an unknown distribution. Unlike previous studies, which assume…