Concept

Vertex (graph theory)

Related publications (183)

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Song Recommendation with Non-Negative Matrix Factorization and Graph Total Variation

Pierre Vandergheynst, Kirell Maël Benzi, Xavier Bresson, Vasilis Kalofolias

This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode ...

Ieee2016

On random subgraphs of Kneser and Schrijver graphs

Andrei Kupavskii

A Kneser graph KG(n,k) is a graph whose vertices are in oneto-one correspondence with k -element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect. A famous result due to Lowisz states that the chromatic num ...

Academic Press Inc Elsevier Science2016

A Precise Threshold For Quasi-Ramsey Numbers

János Pach

We consider the variation of Ramsey numbers introduced by Erdos and Pach [J. Graph Theory, 7 (1983), pp. 137-147], where instead of seeking complete or independent sets we only seek a t-homogeneous set, a vertex subset that induces a subgraph of minimum de ...

Siam Publications2015

When Can Two Unlabeled Networks Be Aligned Under Partial Overlap?

Matthias Grossglauser, Ehsan Kazemi, Lyudmila Yartseva

Network alignment refers to the problem of matching the vertex sets of two unlabeled graphs, which can be viewed as a generalization of the classic graph isomorphism problem. Network alignment has applications in several fields, including social network an ...

2015

Orchestration Graphs

Pierre Dillenbourg

By modeling pedagogical scenarios as directed geometrical graphs and proposing an associated modeling language, this book describes how rich learning activities, often designed for small classes, can be scaled up for use with thousands of participants. Wit ...

EPFL Press2015

Curve Graphs On Surfaces Of Infinite Type

Hugo Parlier, Ariadna Fossas Tenas

We define and study analogs of curve graphs for infinite type surfaces. Our definitions use the geometry of a fixed surface and vertices of our graphs are infinite multicurves which are bounded in both a geometric and a topological sense. We show that the ...

Suomalainen Tiedeakatemia2015

Saturated simple and k-simple topological graphs

János Pach, Jan Kyncl

A simple topological graph G is a graph drawn in the plane so that any pair of edges have at most one point in common, which is either an endpoint or a proper crossing. G is called saturated if no further edge can be added without violating this condition. ...

Elsevier Science Bv2015

Homometric sets in trees

Radoslav Fulek, Slobodan Mitrovic

Let G = (V, E) denote a simple graph with vertex set V and edge set E. The profile of a vertex set V' subset of V denotes the multiset of pairwise distances between the vertices of V'. Two disjoint subsets of V are homometric if their profiles are the same ...

Academic Press Ltd- Elsevier Science Ltd2014

Using Pareto optimality to explore the topology and dynamics of the human connectome

Jean-Philippe Thiran, Alessandra Griffa, Patric Hagmann, Olaf Sporns

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resu ...

Royal Soc2014

Exploring the Volumetric City. A Methodology for Investigating the Topology and Morphology of Surface and Subsurface Urban Spatial Networks

Michael Robert Doyle

The urban underground has historically been developed as a series of sporadic responses to surface land shortage or to hide unsightly urban activities (Parriaux et al 2004; 2010). The Deep City project at the École polytechnique fédérale de Lausanne in Swi ...

2014