Lab · Stochastic block model随机块模型练习 · 随机块模型
When do Arts and Engineering stop talking?文学院和工程学院什么时候不再说话？
A student-union survey asks 40 students, 20 in Arts and 20 in Engineering, one yes-or-no question: did you talk with this person last month? Circles are Engineering. Squares are Arts. Talks are more common inside a faculty than across. The blank between the two clouds is only where the dots were placed so the lines can be read. The faculties were named before any line was drawn. That way of drawing the talks is a stochastic block model: groups first, then a chance of a talk that depends only on whether the two students share a faculty.学生会问了 40 名学生，文学院 20 人、工程学院 20 人，一个是非题：上个月你和这个人说过话吗？圆是工程学院，方是文学院。学院内部的谈话比跨学院更多。两团之间的空白，只是为了把线看清楚，才把点放开。学院在任何一条线画出之前就定了。这种画谈话的办法叫随机块模型：先分组，再按两人是不是同一个学院，决定说过话的机会。
Why it matters.为什么要紧。 The two clouds can look like two faculties that never meet, and still be one conversation if a single Arts–Engineering talk remains. The sliders set the chance of those talks. They do not explain why a real campus looks split.两团可以看起来像两个从不碰面的学院，但只要还剩一次跨学院的谈话，它们仍是同一场对话。滑块设定这些谈话的机会。它们并不解释真实校园为何看起来分开。
Try this试一试 Keep talks inside a faculty at 0.25, then set Arts–Engineering talks to zero. Watch whether the students fall into two conversations, and what share of talks stays inside a faculty.把学院内部的谈话留在 0.25，再把跨学院的谈话设为零。看学生会不会分成两场谈话，以及谈话里有多少留在学院内部。
How to read the chart怎么读这张图
If you read this wrong要是读错了
If the student union tells the two faculties that the blank between the clouds means Arts and Engineering do not talk, they may drop a joint first-year seminar. The blank is where the dots were placed. Separation is missing talks, and the faculty names were on the sheet before any line was drawn.如果学生会告诉两个学院，两团之间的空白表示文学院和工程学院不说话，他们可能会取消一门共同的一年级研讨课。空白是点被放置的位置。分开来的是缺失的谈话，学院的名字在任何一条线画出之前就在表上。
What this picture is enough for这张图够说明什么
Enough to see that lowering the chance of an Arts–Engineering talk changes whether the 40 students are one conversation or two.够用来看见：降低文学院和工程学院之间谈话的机会，会改变这 40 名学生是一场谈话还是两场。
Not enough for a report that the faculties have split. It still has to use talks the survey recorded, and find the groups instead of being handed Arts and Engineering in advance.不够写一份“两个学院已经分开”的报告。报告仍要用调查记下的谈话，并且自己找出分组，而不是事先拿到文学院和工程学院的名单。
The equation, and where it stops式子、假设和边界
Every possible pair of students answers independently, yes or no, with the chance you set for “same faculty” or “different faculties.” That yes-or-no is a Bernoulli draw. Nobody is asked whether they talked to themselves. Changing either chance also changes how many talks you expect in total.每一对学生都独立地回答有没有说过话，机会按你设的“同一学院”或“不同学院”来。这个是或否，就是一次伯努利抽取。没有人被问到自己跟自己说过话没有。改其中任何一个机会，也会改掉你预期会有多少次谈话。
A component is a set of students joined by a chain of talks. The “inside a faculty” share is same-faculty talks divided by all talks. It is not assortativity, which would ask whether same-faculty talks are more common than chance. Even when the two chances are equal, the expected share is 380/780 ≈ 48.7%, because there are 380 same-faculty pairs and 400 cross-faculty pairs.连通分量是被一串谈话连在一起的一组学生。“学院内部”的占比，是同一学院的谈话除以全部谈话。它不是同配性。同配性要问的是：同一学院的谈话是不是比碰巧更多。就算两个机会相等，预期占比仍是 380/780 ≈ 48.7%，因为同一学院的点对有 380 个，跨学院的有 400 个。
The faculties are handed to you. The page does not discover them. The picture shows a mixing pattern. It cannot show that students chose similar friends, or that one friend’s habits changed another’s. Nothing on this page updates a student’s state from their neighbors. That comes on the next page.学院是交给你的，这一页并不去发现它们。图只显示谈话怎么混合。它不能说明学生挑选了相似的朋友，也不能说明一个朋友改变了另一个人。这一页没有任何学生会因为邻居而改变状态。那是下一页的事。
Easy to get wrong.容易踩的坑。 One mistake is to treat the empty space between the circles and the squares as a result. The positions are fixed so the talks can be read. Another is to call the within-faculty share “assortativity.” It is just a fraction of the talks. When the two chances are equal, that fraction is still not one half, because there are 380 same-faculty pairs and 400 cross-faculty pairs. A third is to infer that students chose similar partners. The faculties were assigned before any talk was drawn.一个错，是把圆和方之间的空白当成结果。位置是固定的，为的是看清谈话。另一个错，是把学院内部的占比叫成“同配性”。它只是谈话里的一个比例。两个机会相等时，这个比例仍不是一半，因为同一学院的点对有 380 个，跨学院的有 400 个。第三个错，是推断学生挑选了相似的朋友。学院是在任何谈话画出之前就指定的。