We present the theory of sequences of random graphs and their convergence to limit objects. Sequences of random dense graphs are shown to converge to their limit objects in both their structural properties and their spectra. The limit objects are bounded symmetric functions on [0,1]2. The kernel functions define an equivalence class and thus identify collections of large random graphs who are spectrally and structurally equivalent. As the spectrum of the graph shift operator defines the graph Fourier transform (GFT), the behavior of the spectrum of the underlying graph has a great impact on the design and implementation of graph signal processing operators such as filters. The spectra of several graph limits are derived analytically and verified with numerical examples.
Original languageEnglish
Title of host publication25th European Signal Processing Conference, EUSIPCO 2017
Place of PublicationPiscataway, NJ
PublisherIEEE
Pages365-369
Number of pages5
ISBN (Electronic)978-0-9928626-7-1
DOIs
Publication statusPublished - 2017
EventEUSIPCO 2017: 25th European Signal Processing Conference - Kos Island, Greece
Duration: 28 Aug 20172 Sep 2017
Conference number: 25
https://www.eusipco2017.org/

Conference

ConferenceEUSIPCO 2017
Abbreviated titleEUSIPCO
CountryGreece
CityKos Island
Period28/08/172/09/17
Internet address

    Research areas

  • Graph signal processing, random graphs, graph limits, graphon

ID: 38553664