Lab · Stochastic block model随机块模型实验 · 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, a yes-or-no question: did you talk with this person in the last month? Circles are Engineering. Squares are Arts. Talks are more common inside a faculty than across. The blank between the two clouds is just where the dots were placed on the page. The groups were named before any line was drawn. That recipe is a stochastic block model.学生会问了 40 名学生，文学院 20 人、工程学院 20 人，一个是否题：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，只是点被放在纸上的位置。组的名字在任何一条线画出之前就定了。这个配方叫做随机块模型。
Why this matters.为何重要。 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。
Read the chart读这张图
If you misread this读错了会怎样
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。
Enough, and not enough够用，以及不够
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。
Equations, assumptions, and limits方程、假设与限度
This is a two-block stochastic block model: every possible edge is an independent Bernoulli draw with the selected group-pair probability. There are no self-loops. Changing either probability also changes expected network density.这是两块随机块模型：每条可能的边按所选的组对概率独立地做伯努利抽取。没有自环。改变任一概率也会改变期望密度。
A component is a set of nodes joined by paths. The within-group share counts observed same-group edges divided by all observed edges; it is not an adjusted assortativity coefficient. Even when both probabilities are equal, the expected fraction is 380/780 ≈ 48.7%, because there are 380 same-group and 400 cross-group pairs.连通分量是由路径连在一起的一组节点。组内占比是观察到的同组边数除以全部边数；它不是调整后的同配系数。即使两个概率相等，期望比例仍是 380/780 ≈ 48.7%，因为同组点对有 380 个，跨组点对有 400 个。
The groups are supplied, not discovered by an algorithm. This model illustrates mixing patterns; it cannot establish that homophily or social influence caused a real network. There is no diffusion process in this experiment: nothing here updates a node’s state from its neighbors.组是给定的，不是算法发现的。这个模型说明混合模式；它不能确立同质性或社会影响造成了真实网络。本实验里没有扩散过程：没有任何节点的状态会随邻居更新。
Common pitfall.常见陷阱。 One is to treat the empty space between the circles and the squares as a result. Positions are fixed so the ties are readable. Another is to call the within-group share “assortativity.” It is a raw fraction of edges. When the two probabilities are equal, that fraction is still not one half, because there are 380 same-group pairs and 400 cross-group pairs. A third is to infer that actors chose similar partners. The groups were assigned before any edge was drawn.一个陷阱是把圆和方之间的空白当成结果。位置是固定的，为的是看清连边。另一个是把组内占比叫成“同配性”。它只是边的原始比例。两个概率相等时，这个比例仍不是一半，因为同组点对 380 个，跨组点对 400 个。第三个是推断行动者选择了相似的伙伴。组是在任何边出现之前指定的。