793 research outputs found
Continuum Cascade Model of Directed Random Graphs: Traveling Wave Analysis
We study a class of directed random graphs. In these graphs, the interval
[0,x] is the vertex set, and from each y\in [0,x], directed links are drawn to
points in the interval (y,x] which are chosen uniformly with density one. We
analyze the length of the longest directed path starting from the origin. In
the large x limit, we employ traveling wave techniques to extract the
asymptotic behavior of this quantity. We also study the size of a cascade tree
composed of vertices which can be reached via directed paths starting at the
origin.Comment: 12 pages, 2 figures; figure adde
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