PPT-On the degree distribution of random planar graphs

Angelika Steger j oint work with Konstantinos Panagiotou SODA11 TexPoint fonts used in EMF Read the TexPoint manual before you delete this box A A A A A Random Graphs . Each edge is chosen independently with probability propor tional to the product of the expected degrees of its endpoints We examine the distribution of the sizesvolumes of the connected components which turns out depending primarily on the average d Carla . Binucci. , Emilio Di Giacomo, . Walter Didimo, Fabrizio Montecchiani, Maurizio . Patrignani. , . Ioannis. G. . Tollis. Fan-planar drawings. Fan-planar drawings. Given a graph G, a . fan-planar drawing . Network Science: Random Graphs . 2012. Prof. Albert-László Barabási. Dr. Baruch Barzel, Dr. Mauro Martino. RANDOM NETWORK MODEL. Network Science: Random Graphs . 2012. Erdös-Rényi model (1960). Advanced Kernelization Techniques. Bart . M. P. . Jansen. Insert. «. Academic. unit» . on every page:. 1 Go to the menu «Insert». 2 Choose: Date and time. 3 Write the name of your faculty or department in the field «Footer». Minors, . Bidimensionality. ,. & Decomposition. r. r. Erik Demaine. MIT. Goals. How far . beyond planar graphs . can we go?. Graphs excluding. a fixed minor. Powers thereof. Build . general approximation frameworks . TJTSD66: Advanced Topics in Social Media. (Social . Media . Mining). Dr. WANG, Shuaiqiang @ CS & IS, JYU. Email: . shuaiqiang.wang@jyu.fi. Homepage: . http://users.jyu.fi/~swang/. Why should I use network models?. Node Differential . Privacy . Sofya. . Raskhodnikova. Penn State University. Joint work with. . . Shiva . Kasiviswanathan. . (. GE Research. ),. . Kobbi. . Nissim. . (. Ben-Gurion U. and Harvard U.. . Intro problem- 3 houses and 3 utilities.  K. 3,3. problem: Can 3 houses be connected to 3 utilities so that no 2 lines cross?. Similarly, can an isomorphic version of K. 3,3. be drawn in the plane so that no two edges cross?. Eyal. Ackerman. University of Haifa and . Oranim. College. Drawing graphs in the plane. Consider drawings of graphs in the plane . s.t. .. No loops or parallel edges. Vertices .  distinct points. Daniel Lokshtanov. Based on joint work with Hans Bodlaender ,Fedor Fomin,Eelko Penninkx, Venkatesh Raman, Saket Saurabh and Dimitrios Thilikos. Background. Most interesting graph problems are . NP-hard. Planar graphs. 2. Planar graphs. Can be drawn on the plane without crossings. Plane graph: planar graph, given together with an embedding in the plane. Many applications…. Questions:. Testing if a graph is planar. Random Graphs. Random graphs. Erdös-Renyi. model . One of several models …. Presents a theory of how social webs are formed.. Start with a set of isolated nodes. Connect each pair of nodes with a probability. Erdős-Rényi. Random model, . Watts-. Strogatz. Small-world, . Barabási. -Albert Preferential attachment, . Molloy-Reed . Configuration model . and . Gilbert . Random . G. eometric model. Excellence Through Knowledge. Author: M.E.J. Newman. Presenter: Guoliang Liu. Date:5/4/2012. Outline. Networks in the real world. Properties of networks. Random graphs. Exponential random graphs and Markov graphs. The small-world model.