This talk on Random Graphs and Complex Networks was held on Friday November 11, 2016 in MC 4020. The talk was given by Frieda Rong.

## Abstract

From the graph of Facebook friendships to the neurons inside your brain, networks are all around us. We’ll go over some surprising *connections* in network theory and see some of the following:

## Outline

Random graphs

Phase transitions of the Erdos-Renyi random graph, and emergence of the so-called “giant” component

If time permits, discovering that the uniqueness of this component approaches probability of $\frac{5\pi}{18}$

The Rado graph and its connection to first order logic on graphs

Spectral theory of general undirected graphs

What the eigenvalues of the adjacency and Laplacian matrices say about the properties of a graph

Connections to computer vision and dimensionality reduction