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Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…

Social and Information Networks · Computer Science 2013-05-28 Charalampos E. Tsourakakis

Many complex systems can be represented as networks, and how a network breaks up into subnetworks or communities is of wide interest. However, the development of a method to detect nodes important to communities that is both fast and…

Physics and Society · Physics 2015-05-27 Yang Wang , Zengru Di , Ying Fan

The application of the network approach to the urban case poses several questions in terms of how to deal with metric distances, what kind of graph representation to use, what kind of measures to investigate, how to deepen the correlation…

Other Condensed Matter · Physics 2007-05-23 Sergio Porta , Paolo Crucitti , Vito Latora

We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…

Networking and Internet Architecture · Computer Science 2008-04-16 Priya Mahadevan , Dmitri Krioukov , Kevin Fall , Amin Vahdat

Learning fair graph representations for downstream applications is becoming increasingly important, but existing work has mostly focused on improving fairness at the global level by either modifying the graph structure or objective function…

Social and Information Networks · Computer Science 2022-12-26 April Chen , Ryan Rossi , Nedim Lipka , Jane Hoffswell , Gromit Chan , Shunan Guo , Eunyee Koh , Sungchul Kim , Nesreen K. Ahmed

For every positive integer $n$, we find a complete classification for planar graphs according to the collection of numbers of common neighbours for every $n$-tuple of distinct vertices. Our results expand the literature on planar graphical…

Combinatorics · Mathematics 2025-11-25 Riccardo W. Maffucci

Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…

Discrete Mathematics · Computer Science 2022-07-04 Timo Gervens , Martin Grohe

A new class of distances for graph vertices is proposed. This class contains parametric families of distances which reduce to the shortest-path, weighted shortest-path, and the resistance distances at the limiting values of the family…

Combinatorics · Mathematics 2011-01-25 Pavel Chebotarev

We study the neighborhood polynomial and the complexity of its computation for chordal graphs. The neighborhood polynomial of a graph is the generating function of subsets of its vertices that have a common neighbor. We introduce a…

Combinatorics · Mathematics 2023-06-22 Helena Bergold , Winfried Hochstättler , Uwe Mayer

Many degree sequences can only be realised in graphs that contain a `ds-completable card', defined as a vertex-deleted subgraph in which the erstwhile neighbours of the deleted vertex can be identified from their degrees, if one knows the…

Combinatorics · Mathematics 2018-10-08 Andrew M. Steane

We consider ad-hoc networks consisting of $n$ wireless nodes that are located on the plane. Any two given nodes are called neighbors if they are located within a certain distance (communication range) from one another. A given node can be…

Networking and Internet Architecture · Computer Science 2018-11-29 Erdem Koyuncu , Hamid Jafarkhani

In colored graphs, node classes are often associated with either their neighbors class or with information not incorporated in the graph associated with each node. We here propose that node classes are also associated with topological…

Social and Information Networks · Computer Science 2019-11-19 Roy Abel , Idan Benami , Yoram Louzoun

Learning graph-structured data with graph neural networks (GNNs) has been recently emerging as an important field because of its wide applicability in bioinformatics, chemoinformatics, social network analysis and data mining. Recent GNN…

Machine Learning · Computer Science 2021-12-16 Cheolhyeong Kim , Haeseong Moon , Hyung Ju Hwang

In this paper, we consider the problems from the area of sublinear-time algorithms of edge sampling, edge counting, and triangle counting. Part of our contribution is that we consider three different settings, differing in the way in which…

Data Structures and Algorithms · Computer Science 2022-04-13 Jakub Tětek , Mikkel Thorup

The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…

Computation and Language · Computer Science 2019-06-18 Andrey Kutuzov , Mohammad Dorgham , Oleksiy Oliynyk , Chris Biemann , Alexander Panchenko

Graphs are widely used as a popular representation of the network structure of connected data. Graph data can be found in a broad spectrum of application domains such as social systems, ecosystems, biological networks, knowledge graphs, and…

Machine Learning · Computer Science 2021-05-04 Feng Xia , Ke Sun , Shuo Yu , Abdul Aziz , Liangtian Wan , Shirui Pan , Huan Liu

Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in…

Machine Learning · Computer Science 2019-09-19 Leo Liberti

We are given the adjacency matrix of a geometric graph and the task of recovering the latent positions. We study one of the most popular approaches which consists in using the graph distances and derive error bounds under various…

Statistics Theory · Mathematics 2020-08-13 Ery Arias-Castro , Antoine Channarond , Bruno Pelletier , Nicolas Verzelen

A graph labeling assigns values to the components of a graph (vertices, edges, etc.). In particular, distance magic labelings have been widely studied in undirected graphs. In such a labeling, the vertices are labeled with unique values…

In a labeling scheme the vertices of a given graph from a particular class are assigned short labels such that adjacency can be algorithmically determined from these labels. A representation of a graph from that class is given by the set of…

Computational Complexity · Computer Science 2018-02-09 Maurice Chandoo