PPT-Graphs-Part II

Depth First Search DFS We Already Covered Breadth First SearchBFS Traverses the graph one level at a time Visit all outgoing edges from a node before you go deeper Needs a queue BFS creates a tree called BFSTree. There is actually only one main program the spe ci64257c layout algorithms implemented as plugins Thus the yl ar gely share all of the same commandline options dot draws directed graphs It works well on D AG sa nd other graphs that can be drawn as h Sometimes, two graphs have exactly the same form, in the sense that there is a one-to-one correspondence between their vertex sets that preserves edges. In such a case, we say that the two graphs are . 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). Isabelle Stanton, UC Berkeley. Gabriel . Kliot. , Microsoft Research XCG. Modern graph datasets are huge. The web graph had over a trillion links in 2011. Now?. . facebook. has “more than 901 million users with average degree 130”. 2-3. In addition to the histogram, the frequency polygon, and the . ogive. , several other types of graphs are often used in statistics. They are the bar graph, Pareto chart, time series graph, and pie chart. . Angelika Steger. (j. oint. . work. . with. . Konstantinos . Panagiotou. , SODA‘11. ) . . TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. Random Graphs . L. á. szl. ó. . Lov. á. sz. Eötvös Loránd University. Budapest . September 2012. 1. September 2012. Tur. á. n’s Theorem . (special case proved by Mantel):. . G. contains no triangles .  #edges. Daniel A. Spielman. Yale University. AMS Josiah Willard Gibbs Lecture. January . 6. , 2016 . From Applied to Pure Mathematics. Algebraic and Spectral Graph Theory. . . Sparsification. :. a. pproximating graphs by graphs with fewer edges. Misleading Graphs. Good . graphs are extremely powerful tools for displaying large quantities . of complex . data; they help turn the realms of information available today . into knowledge. . But, unfortunately, some graphs deceive or mislead. This . Graphs.  . Graphs . capture . much more detail than numerical summaries, so very useful for learning about data and communicating its features.. At the same time, graphical interpretation isn’t standard in the way that numerical summaries are, and our eyes can fool us.. Daniel A. Spielman. Yale University. AMS Josiah Willard Gibbs Lecture. January . 6. , 2016 . From Applied to Pure Mathematics. Algebraic and Spectral Graph Theory. . . Sparsification. :. a. pproximating graphs by graphs with fewer edges. 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. The vertical scale is too big or too small, or skips numbers, or doesn’t start at zero.. The graph isn’t labeled properly.. Data is left out.. But some real life misleading graphs go above and beyond the classic types. Some are intended to mislead, others are intended to shock. And in some cases, well-meaning individuals just got it all plain wrong. These are some of my favorite recent-history misleading graphs from real life..