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In the spirit of past CCEGN workshops (CCEGN-2018, CCEGN-2017, CCEGN-2016), the workshop "Critical and Collective Effects in Graphs and Networks - 2019" (CCEGN-2019) continues to explore the topics at the interface between network science, statistical physics, and random graphs. The CCEGN-2019 will bring together top researchers working in these areas. The workshop aims at facilitating the transfer of ideas, insights and interdisciplinary approaches to tackle new and exciting problems in random graphs and real networks. Topics include: Spreading phenomena and other dynamical process on networks, Griffiths phases and spectral methods Metric structure of random graphs, and spatially embedded random graphs Random graphs with quenched disorder, microcanonical and canonical ensembles of random graphs, phase transitions, belief propagation and related questions Statistical methods in interdisciplinary applications: social and ecological networks, genomic networks, neuroscience There are two traditional features of the CCEGN workshops that the past attendees mostly enjoyed: (i) the relaxed schedule of talks to allocate a plenty of time for scientific discussions and exchange of ideas, and (ii) the high quality of the presentations -- all talks are invited and are given by top experts in their fields, and each talk is 1 hour including questions. Discussion panels on various topics may be formed by the organizers if there is a substantial interest among the attendees. The list of speakers: Marc Barthelemy (Institut de Physique Théorique, Saclay, France) Ginestra Bianconi (Queen Mary University, London, UK) Zdzislaw Burda (AGH University of Science and Technology, Kraków, Poland) Sergey Dorogovtsev (Aveiro University, Portugal, and A.F. Ioffe Institute, St. Petersburg, Russia) Ernesto Estrada (University of Strathclyde, Glasgow, UK) Alex Fornito (Monash University, Melbourne, Australia) Laetitia Gauvin (ISI Foundation, Torino, Italy) James Gleeson (University of Limerick, Ireland) Joaquín Goñi (Purdue University, West Lafayette, IN, USA) Clara Granell (University of Barcelona, Spain) Roger Guimerà (Universitat Rovira i Virgili, Tarragona, Spain) Byungnam Kahng (Seoul National University, Seoul, Korea) Pavel Krapivsky (University of Boston, Boston, USA) Vito Latora (Queen Mary University, London, UK) Sergei Maslov (University of Illinois at Urbana-Champaign, USA) Adilson Motter (Northwestern University, Evanston, IL, USA) Fragkiskos Papadopoulos (Cyprus University of Technology, Limassol, Cyprus) Tiago Peixoto (University of Bath, UK, and ISI Foundation, Turin, Italy) M. Ángeles Serrano (University of Barcelona, Spain) Zoltan Toroczkai (University of Notre Dame, Notre Dame, IN, USA) The overview yet in-depth format of talks provides an excellent opportunity for researchers at early stages of their carriers to learn about recent cutting-edge developments in network science and adjacent areas, so that PhD students, postdocs and young researchers working in these areas are encouraged to attend the workshop. The workshop attendees are encouraged to submit posters on their research as the workshop will feature poster sessions with lightning presentations. A limited number of travel grants will be available on a competitive basis. To submit a poster and/or to apply for a travel grant, please contact the workshop organizing committee at firstname.lastname@example.org. The workshop will take place during 6 - 10 of May, 2019 at Les Houches Physics School located in the Chamonix valley of French Alps. The instructions how to get to the school are available at the school website: https://www.houches-school-physics.com/practical-information/access/. Participants arrive Sunday evening (May 5), the talks start Monday morning (May 6) and end Friday noon (May 10).