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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…

Machine Learning · Statistics 2018-09-11 Zhen Zhang , Mianzhi Wang , Yijian Xiang , Yan Huang , Arye Nehorai

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…

Combinatorics · Mathematics 2024-04-04 Shuhei Tsujie , Ryo Uchiumi

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…

Data Structures and Algorithms · Computer Science 2022-11-08 Josep Díaz , Öznur Yaşar Diner , Maria Serna , Oriol Serra

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…

Statistical Mechanics · Physics 2009-12-19 Jun Wu , Mauricio Barahona , Yuejin Tan , Hongzhong Deng

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…

Spectral Theory · Mathematics 2025-09-18 Alessio Catanzaro , Rajat Subhra Hazra , Diego Garlaschelli

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…

Machine Learning · Computer Science 2020-01-22 Benedek Rozemberczki , Rik Sarkar

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…

Machine Learning · Computer Science 2018-10-16 Yihan Gao , Chao Zhang , Jian Peng , Aditya Parameswaran

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…

Information Theory · Computer Science 2016-11-17 Michael Rabbat , Mario Figueiredo , Robert Nowak

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…

Information Theory · Computer Science 2020-08-24 B. Subbareddy , Aditya Siripuram , Jingxin Zhang

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…

Applications · Statistics 2021-06-23 Shangsi Wang , Jesús Arroyo , Joshua T. Vogelstein , Carey E. Priebe

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…

Data Structures and Algorithms · Computer Science 2025-07-01 Taha Ameen , Bruce Hajek

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…

Machine Learning · Statistics 2014-05-26 Shuheng Zhou

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…

Probability · Mathematics 2015-06-11 Paul Balister , Béla Bollobás , Svante Janson

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…

Statistical Mechanics · Physics 2010-04-27 Allon G. Percus , Gabriel Istrate , Bruno Goncalves , Robert Z. Sumi , Stefan Boettcher

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…

Combinatorics · Mathematics 2013-11-13 Svante Janson , Simone Severini

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…

Computational Geometry · Computer Science 2013-04-10 Abbas Mehrabian , Nick Wormald

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…

Discrete Mathematics · Computer Science 2016-01-12 René van Bevern , Robert Bredereck , Jiehua Chen , Vincent Froese , Rolf Niedermeier , Gerhard J. Woeginger

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…

Statistics Theory · Mathematics 2026-04-07 Dong Huang , Chenyang Tian , Pengkun Yang

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…

Combinatorics · Mathematics 2007-05-23 Remco van der Hofstad , Joel Spencer

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…

Social and Information Networks · Computer Science 2019-03-05 Feng Ji , Wenchang Tang , Wee Peng Tay , Edwin K. P. Chong