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Title: Properties of generalized hooking networks

Abstract: Hooking networks are random networks grown from a set of graphs called blocks, each block with a labelled vertex called a hook. At each step in the growth of the network, a vertex called a latch is chosen from the hooking network and a block is chosen from the set of blocks. A copy of the chosen block is then attached to the network by fusing together its hook with the chosen latch. Hooking networks generalize several types of random trees, which can be thought of as hooking networks grown from a single edge as the only block.


In this talk I will present results for certain properties of hooking networks. This includes a normal limit law for the degree distributions of hooking networks. In some cases more can be proven, including convergence of moments of the degree distributions, and central limit theorems for the depth of the n'th latch chosen and the depth of a vertex chosen uniformly at random from the network.


This is joint work with Cecilia Holmgren and Hosam Mahmoud.

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