Hi, folks. So, let's just go through a quick summary of some of the things we've covered in Week 1. So, one of the most important things we started with was the fact that many relationships of all types, social, political, economic, are networked. So, when people are interacting, when firms are interacting, when countries are interacting, when different kinds of organizations are interacting, often, they're embedded in a network structure. And most importantly, understanding those network structures is very important in understanding and predicting outcomes and behavior. And that's part of where the course is going and we'll get there eventually, so the, the latter part of the course will be looking at this in detail. Second important point, networks are very complex. There's many different networks on the same, some set of nodes and so it's going to be difficult to describe networks without looking at some sort of simple sufficient statistics or summary statistics. And things like degree distributions actually capture a lot of what's going on, clustering, how well connected are things on a local level, do we see lots of triangles, do we see few triangles? Diameter, is this a network where it's very hard to go from one node to another or, are all nodes relatively close together? There's a number of different things which can be used to describe networks, and we'll keep track of those, and, and we'll be looking at those. And, and those kinds of things are eventually going to tie to properties of Networks and how they influence behavior, what kinds of things emerge from the network. another important point that we covered was that tree-like structures tend to be generated by random links, and those lead to very short paths. So, if you've got simple tree structures underlying things, then the branching process leads to diameters, path links that are logarithmic in nature, so much shorter than looking, marching linearly in terms of the number of nodes. And so, just by putting simple tree structures which are going to arise under a number of different kinds of formation processes. So, many different ways in which we can form networks are actually going to lead to an underlying tree structure that's going to lead naturally to short kinds of paths. Last point, many observed social networks have simple kinds of properties to them. And in particular, we tend to see very dense connections, things like triads or cliques on local levels when we look at friendships, when we look at different kinds of interactions in social settings. Many people that I know, will know each other and, and vice versa. And so, that's going to turn out to be important in information transmission and how people end up looking to each other to, to, to choose behaviors and will be something else that we look at quite a bit, going down the road.