So we're going to begin by giving you a basic idea about what a network is, and why we want to study networks. So a network is simply a set of objects, which we call nodes, that have some relationships between each other, which we call edges. And why do we want to study networks? So the first reason why we want to study networks, is because networks are everywhere. So what I'm going to do, is I'm going to show you how network shows up in a bunch of different settings. So the first kind of network that we are going to look at are social networks. And in social networks the nodes are people, and the connections between the nodes represent some type relationship between the people in the network. So here we see an example of 34 people who belong to a karate club, and the network represents friendship between them. In this example, node number one, which you see right here, is the instructor in the karate club and everybody else is a student in the karate club. This other example is a network of friendship, marital tie, and family tie among 2,200 people. Here the edges are colored to represent the particular type of relationship between the nodes. And then next we have an e-mail communication network. So the other two networks we saw were in relationships that were happening in the offline world, but networks can also be constructed based on relationships that happen in the online world. So here in this example, we have a network between 436 HP employees and the edges represent communication through email. We can also have transportation and mobility networks. So in this example, we see a network of directed flights between the different airports around the world. And there's human mobility network that is based on the location of dollar bills using the words George website, where people look at their dollar bills, tells the website where they are located. And then this bill can be track when other people update the location of this bill. We can see this bill has travel throughout the United States, and here is the network I gets more by tracking bills movement. And here we have a network that represents the bus transportation network of Ann Arbor. And here the edges represent direct bus routes from one stop to the next stop. Here also information networks, so in this example, we see network where the nodes are political blogs and then edges represent connections between the blogs through URLs. So who links to, what blog links to which blog? And what we see here is that they're colored by one of their left wing or right wing. And what we see is that left-wing blogs tend to connect mainly to left-wing blogs, and right-wing blogs tend to connect mainly to right-wing blogs, but there are not a lot of connections that go from one to the other. So we call this clustering, there's a lot of clustering between the two types of blogs. Here is the network that represents the Internet connectivity, and here's a network between Wikipedia articles about climate change. The ideas also represent URL connections or direct connections between one article in the next. And here we can also see that there is some clustering happening. So the colors represent different sub-topping within climate change, and we can see that they are clustered by the different sub-toppings. Networks also show up in biology, so here's an example of a protein to protein interaction. So the nodes are proteins and they're connected by where they interact with each other. And here is a network that represent a food web, so what animals eat what animals. And I could continue showing more and more different types of networks. So we can have financial networks, co-authorship networks, trade networks, citation network, and on, and on, and on. So this can give you a sense that networks tend to show up in all different types of context. In this course, we're going to focus mainly on social networks, but networks in general are useful to study in many other types of context. Okay, so networks tend to be everywhere, but is that enough of reason why we should study them? What kinds of things can we do when we take some complex phenomena and represented as a network, is there something we can understand better about this phenomena by studying the structure of the network? And the answer is, yes, there are plenty of things we can do. So I'm going to give you some examples. Let's go back to this email communication network among the 436 HP employees. The kinds of questions that we can answer by looking at the structure of the network are things like, if there's a rumor that starts in some part of the network, is it likely to spread through the whole network? And who are the most influential people in this organization? Is the rumor that's starting on say, some node that's sort of like on the outskirts of the network more or less likely to be spread than if it were to be started by somebody who's more central to the network, like someone around this area? These are the kinds of things that we can start to analyze and understand by looking at the structures of a network. Looking at, again, the friendship network between the karate club members, we can answer things like, is this club likely to split into two different clubs? And actually the story is that, this is exactly what happens. If you could try to guess which member is going to join which club after it splits, you can look at the structure of this network and make a pretty educated guess. And it turns out that, as you can probably see from just looking at this network, the division between the club happens around here where the nodes on the left side of this line go to one club, and then the ones on the right go to the other club. If we look at a network of transportation network of direct flights around the world, can we answer the questions like, if there's an epidemic or a virus spreading in the world, are there airports that we have to pay more attention to than others? Or if there are certain parts of the world that are harder to reach through air transportation, what are key connections we can make to make those areas easier to reach? These are all questions that we can study by looking at the structure of social network, and a lot of which we're going to be, and asking again later on in the course, and giving you the tools that you need to be able to begin to understand these types of questions. So in summary, many complex structures can be modeled through networks. So we saw examples from social networks from biology networks, transportation networks, and so on. And by studying the structure of these networks, we can start to answer questions that are pretty complex. And that a deal with very complex relationships and networks allow us to make those relationships, or to make those complex phenomena simpler by representing them as a network and then using certain tools that allow us to answer that. And so, in this course we're going to cover some of the basic techniques to study social networks and answer some very interesting questions about them.