1 00:00:00,880 --> 00:00:06,055 Now, that we've learned the two concepts of node degree and connected components, 2 00:00:06,055 --> 00:00:11,155 we can start to apply them immediately to the dining-table's partner data set and 3 00:00:11,155 --> 00:00:15,696 see what insights we can get out of it. First, let's look at degree. 4 00:00:15,696 --> 00:00:19,340 Now we have some choices. This is a directed network, so we can look 5 00:00:19,340 --> 00:00:22,259 at InDegree, OutDegree, or just undirected degree. 6 00:00:22,260 --> 00:00:27,969 Now, why doesn't OutDegree make sense? Well, every girl is naming two other girls 7 00:00:27,969 --> 00:00:32,896 as their as her first and second choice. Therefore, all the nodes are going to have 8 00:00:32,896 --> 00:00:34,568 the same degree. Same OutDegree. 9 00:00:34,568 --> 00:00:38,602 So we don't want OutDegree. Indegree, on the other hand, is a lot more 10 00:00:38,602 --> 00:00:41,619 interesting, because it's a reflection of popularity. 11 00:00:41,620 --> 00:00:46,810 If lots of other girls want to sit with you at the same table, well, that says 12 00:00:46,810 --> 00:00:50,917 something about how desirable you are in this girl storm. 13 00:00:50,918 --> 00:00:59,642 So let's look at that. The degree is calculated automatically, so 14 00:00:59,642 --> 00:01:06,345 you can just go straight to Ranking > Nodes > InDegree. 15 00:01:06,345 --> 00:01:11,353 Now, we could color the nodes by InDegree, but we're going to save color for the 16 00:01:11,353 --> 00:01:15,535 connected components. So let's instead look at size, it's this 17 00:01:15,535 --> 00:01:19,739 little diamond shape here, so I'm going to click on it. 18 00:01:19,740 --> 00:01:24,840 And we can chose the Min and Max size. I'm going to go since these nodes are 19 00:01:24,840 --> 00:01:28,138 sized 5. I'm going to set the Min size a little bit 20 00:01:28,138 --> 00:01:31,167 lower at 2 and the Max size maybe twice that. 21 00:01:31,168 --> 00:01:36,226 There is this option called Spline. And this just says, how does this size 22 00:01:36,226 --> 00:01:40,935 vary as this quantity of interest varies in this case in degrees? 23 00:01:40,936 --> 00:01:47,642 Since the inequality in popularity isn't that large and it's a relatively small 24 00:01:47,642 --> 00:01:53,955 network, this linear relationship is okay. However, if for example, you were looking 25 00:01:53,955 --> 00:01:57,052 at a massive network a directed one such as the web. 26 00:01:57,053 --> 00:02:01,170 And, well, you wouldn't be looking at the whole web, but say a subset of the web. 27 00:02:01,170 --> 00:02:07,697 And there could be one page that has 100,000 in links, and many other pages 28 00:02:07,697 --> 00:02:13,891 that have one in-link or no in-links. And you wouldn't want a node that's 29 00:02:13,891 --> 00:02:19,448 100,000 times bigger than other nodes. It would just obscure your whole 30 00:02:19,448 --> 00:02:24,327 visualizations. In that case, you may want to do something 31 00:02:24,327 --> 00:02:29,530 like a law of linear relationship, something like this. 32 00:02:29,530 --> 00:02:32,600 But for our purposes here, we're just going to go linear. 33 00:02:32,600 --> 00:02:38,417 So, let's apply that, and voila. Instantly, we can see that some girls are 34 00:02:38,417 --> 00:02:43,032 more popular than others. Marion and Eva look like they're most 35 00:02:43,032 --> 00:02:47,503 popular and Hilda Doesn't seem to be doing too poorly either. 36 00:02:47,504 --> 00:02:55,007 Now this is all visual. And if we want to actually look up the 37 00:02:55,007 --> 00:02:58,030 numbers. What is the InDegree of each node? 38 00:02:58,030 --> 00:03:03,336 If we simply go to Data Laboratory. Unfortunately, it doesn't populate the 39 00:03:03,336 --> 00:03:07,134 degree automatically. So we're going to go back to Overview. 40 00:03:07,135 --> 00:03:11,437 And we're going to ask it to calculate the Average degree. 41 00:03:11,438 --> 00:03:17,885 Now, the Average degree is 2, which we sort of knew, because we have 52 edges and 42 00:03:17,885 --> 00:03:21,937 2, 26 nodes, so you can divide 1 by the other. 43 00:03:21,937 --> 00:03:27,280 So nothing surprising there. It has given us the Degree Distribution. 44 00:03:27,280 --> 00:03:30,478 We're actually interested in the In-Degree distribution. 45 00:03:30,479 --> 00:03:39,330 And here, you can see that, for example, two girls have In-Degree 6, but I don't 46 00:03:39,330 --> 00:03:45,623 know, nine girls have In-Degree 2. So that's interesting in and of itself. 47 00:03:45,624 --> 00:03:51,807 However, what is super nice about this is that we can go back to Data Lab. 48 00:03:51,807 --> 00:03:58,845 And now, we actually have the In-Degree and clicking on top here of this sorts 49 00:03:58,845 --> 00:04:03,140 lowest to highest. Let's click again and we have the two 50 00:04:03,140 --> 00:04:07,046 girls who have In-Degree 6 who are Marion and Eva. 51 00:04:07,047 --> 00:04:11,958 So that's a nice way of just getting at the, numbers. 52 00:04:11,958 --> 00:04:16,997 And, also, if you're interested in the Debris Distribution you can have a quick 53 00:04:16,997 --> 00:04:21,318 look like this. Of course, you can export this spreadsheet 54 00:04:21,318 --> 00:04:25,304 and analyze it further as well. So back to the Overview. 55 00:04:25,305 --> 00:04:30,511 What we have is a picture where some girls are more popular than others, but we don't 56 00:04:30,511 --> 00:04:34,858 really know whether there certain cliques or how information might flow. 57 00:04:34,858 --> 00:04:41,186 So, I'm going to start out by asking a question, you now, if someone had some 58 00:04:41,186 --> 00:04:46,470 piece of gossip, one particular girl. Where could that gossip go? 59 00:04:46,470 --> 00:04:53,446 Or if you had a set of girls, would they all be able to hear gossip from everyone 60 00:04:53,446 --> 00:04:56,536 else? And this is precisely the question of who 61 00:04:56,536 --> 00:05:01,124 is in the same strongly connected component, because if you're in the same 62 00:05:01,124 --> 00:05:06,230 strongly connected component with someone else, it means that anything that they 63 00:05:06,230 --> 00:05:09,177 find out can potentially make its way to you. 64 00:05:09,178 --> 00:05:12,550 So let's find the strongly connected components. 65 00:05:12,550 --> 00:05:16,400 I'm going to go back to the Statistics tab. 66 00:05:16,400 --> 00:05:19,999 If you have Filters instead, just make sure you click on Statistics. 67 00:05:20,000 --> 00:05:23,120 And I'm going to click on Connected Components. 68 00:05:23,120 --> 00:05:26,458 I'm going to say Run. And it's going to ask me if I want the 69 00:05:26,458 --> 00:05:31,926 strongly connected components. Which I can get in a Directed graph, or 70 00:05:31,926 --> 00:05:33,940 not. Yes, I do in fact want the strongly 71 00:05:33,940 --> 00:05:37,148 connected components. Because, if you imagine the flow of 72 00:05:37,148 --> 00:05:41,698 information, if one girl says she would like to sit with someone else, but that 73 00:05:41,698 --> 00:05:44,374 one, that person doesn't want to sit with her. 74 00:05:44,374 --> 00:05:48,077 Well, they may also not be willing to share information with her. 75 00:05:48,078 --> 00:05:53,047 So, we really want to take into account the directionality of the edges. 76 00:05:53,048 --> 00:05:56,542 So I'm going to say, okay. And, it's telling me there is one weakly 77 00:05:56,542 --> 00:06:01,441 connected component, which just means if we treat the edges as undirected, everyone 78 00:06:01,441 --> 00:06:04,600 is connected directly or undirectly, which is true. 79 00:06:04,600 --> 00:06:09,424 But we just have a single connected network but it's telling me that there are 80 00:06:09,424 --> 00:06:14,392 actually 11 different strongly connected components, meaning that information 81 00:06:14,392 --> 00:06:18,875 wouldn't circulate throughout the network following directed edges. 82 00:06:18,876 --> 00:06:25,245 So, we're going to close this, and now, let's color the nodes by the strongly 83 00:06:25,245 --> 00:06:30,456 connected components. So, I'm going to go to Partition here, and 84 00:06:30,456 --> 00:06:36,252 I want to partition the Nodes, and I'm going to click Refresh to just get this 85 00:06:36,252 --> 00:06:41,132 new partition. Which should be the Strongly-Connected ID. 86 00:06:41,132 --> 00:06:47,618 And, it's giving me some colors some of these seem a little bit similar, so let me 87 00:06:47,618 --> 00:06:51,538 just see. I'm going to right-click and say Randomize 88 00:06:51,538 --> 00:06:54,930 colors and these look a little bit different. 89 00:06:54,930 --> 00:07:01,784 So I'm going to Apply them. And I think this paints a very, very clear 90 00:07:01,784 --> 00:07:08,877 picture about the dynamics in this in this among this group of girls. 91 00:07:08,878 --> 00:07:15,802 So first of all we have the purple cluster here, where all of these girls may be 92 00:07:15,802 --> 00:07:23,146 sharing information with each other and they also include these two very popular 93 00:07:23,146 --> 00:07:28,502 girls, Marion and Eva. You see this one girl here, Alice, who 94 00:07:28,502 --> 00:07:34,266 names two girls in this cluster, but her color is actually different. 95 00:07:34,266 --> 00:07:40,360 She's in the strongly connected component all by herself because, actually, no one 96 00:07:40,360 --> 00:07:44,032 selected Alice as someone they wanted to sit with. 97 00:07:44,033 --> 00:07:50,670 We see, this little component here of three nodes in blue, Betty, Hilda and 98 00:07:50,670 --> 00:07:55,112 Hazel. All had, well, Hazel had selected Hilda 99 00:07:55,112 --> 00:08:00,960 and vice versa, and Betty had selected Hilda and vice versa. 100 00:08:00,960 --> 00:08:08,154 So they form one strongly connected component a similar dynamic with Jane, 101 00:08:08,154 --> 00:08:13,956 Mary, and Edna. And here is an example with Helen, Jean, 102 00:08:13,956 --> 00:08:17,600 and Robin. So here, you actually have a closed triad, 103 00:08:17,600 --> 00:08:21,880 but what has happened is that Helen and Jean mutually chose each other. 104 00:08:21,880 --> 00:08:26,850 And then, Jean chose Robin as her second choice. 105 00:08:26,851 --> 00:08:32,230 And then, Robin chose Helen. So you can kind of circulate in here. 106 00:08:32,230 --> 00:08:37,456 And then, Ada and Cora are their own strongly connected component, because they 107 00:08:37,456 --> 00:08:42,807 chose each other. So this shows you a bit of the dynamic of, 108 00:08:42,807 --> 00:08:49,560 of [laugh] girls in, in, you know, earlier stages of their lives. 109 00:08:49,560 --> 00:08:55,020 But also, there's some recent research showing that most social networks, when 110 00:08:55,020 --> 00:09:00,558 you're naming friends tend to be fairly asymmetrical like this, and in this case, 111 00:09:00,558 --> 00:09:04,075 because it's a relatively small network, etcetera. 112 00:09:04,075 --> 00:09:07,552 Even just looking at the strongly connected components without applying 113 00:09:07,552 --> 00:09:11,360 community detection algorithms, which is something that we're going to be doing 114 00:09:11,360 --> 00:09:17,420 later on. We can figure out a lot of the dynamic 115 00:09:17,420 --> 00:09:20,373 between the girls.