"Mathematics, to me, is beautiful in the pure sense just for that. It's quite interesting to see human civilization as a network, as a graph, and our relationships as kind of edges in that graph."
"You're the average of the five people that are closest to you. It has a tremendous impact."
"The world has never lived through a period of time of Metcalfe's Law, adoption curves on top of Metcalfe's Law adoption curves, creating Reed's law, which is a ridiculously powerful moment in time."
"Network effect, network effect, network effect."
"Even if you change the width of a network, on the x-axis, you see that the trajectory length is always higher."
"Network effects are when every additional user drives more additional value to all other users."
"Graph theory is all about the study of the properties of these types of networks, and how they can be used to model and solve a whole host of interesting problems."
"Metcalf's Law: the value of a network rises with the square of the number of devices connected to it."
"We are at a whole new level with network analysis, Network Theory, than we ever were prior to 9/11."
"The notion of network is a very powerful way of rephrasing basic issues of social theory, epistemology, and philosophy."
"The network is the next leviathan, hovering above, making fallible men behave in pro-social ways."
"The idea of an assemblage network and distributed agency."
"For many diseases, including substance use disorders, they can often be conceptualized as a failure in network regulation."
"The connectivity of your network is highly correlated with the trait."
"A network is a collection of points joined together by lines."
"You can use the stability or instability of these triads to model what would be the expected outcome or settled state for a network."
"The good thing is that networks provide you a language that you can use through to describe extremely different systems."
"These star-like structures... are what we call hubs in the network; they're nodes that have a lot of connections to other people."
"The amazing thing is that... across any cut, you're going to see this flow."
"The utility of a network increases geometrically as you add more nodes."
"Network theory hypothesizes that central symptoms are really driving the maximum number of other symptoms."
"The idea of six degrees of separation is that everyone in the world is connected to each other by six steps through a friendship network or acquaintances network."
"Of course it doesn't prove that the world is six steps apart but it actually gives you a very good intuition behind how this works."
"The world is not linked like that of course it's much more complicated but this gives you an idea of how fast things can grow and how small the diameter could be if you have this very particular structure."
"It's going to converge to a distribution where you have higher probability at any given time at being on a page that's kind of tightly connected."
"You can know anyone in the world in six steps."
"Nodes with the most edges are the most important or central as they are directly related to plenty of other nodes."
"People who are located in structural holes in the network are more likely to have creative ideas."
"These are networks that as you put more people on the network, they become more efficient."
"And we'll, more or less, end the lecture with the statement of the max-flow min-cut theorem, which is really an iconic theorem in the literature."
"A good rule of thumb is the magic number of 150."
"Every augmented path is going to have at least one critical edge."
"The small world phenomena... even though the network is large, the shortest path lengths are actually quite small."
"The largest connected component occurs exactly when the average degree is greater than one."
"Subgraphs would have rich connectivity structures, both internally and externally through interactions with the rest of the graph."
"We're living in this world where social networks do have a power-law distribution or scale-free distribution."
"The effects of many biological interventions are really network effects."
"If S is equal to one, then every node in the graph belongs to GCC."
"If a node on average has more than one neighbor, there is a gigantic connecting component and they're all connected."
"Clustering coefficient is just the ratio of those closed triangles to the total number of possible triangles."
"We can actually adjust the model a little bit and fix at least the issue with degree distribution."
"We call a two-port network reciprocal when Z12 is equal to Z21."
"Preferential attachment... means that the new node will have a high probability to connect to nodes with high degrees."
"Money goes to money... when somebody comes in and selects friends, it would rather join people with lots of friends."
"The rich get richer, and getting richer much faster than in the random model."
"Attention is something that allows certain parts of the network to concentrate on certain other parts of the network."
"Network Theory... is really about this big idea of connectivity."
"The value of a network is the square of the users or the connections."
"We were engaged by the South Australian police where we did an analysis of distributed networks using network graph theory."