得到與相鄰節(jié)點特征均值相對應(yīng)的節(jié)點表示。這是因為（轉(zhuǎn)換后的）鄰接矩陣權(quán)重，與相鄰節(jié)點特征加權(quán)和的權(quán)重相對應(yīng)。我鼓勵你自己驗證此觀察。
放在一起
現(xiàn)在，我們結(jié)合了自循環(huán)和標(biāo)準(zhǔn)化技巧。此外，我們將重新介紹先前為簡化討論而丟棄的權(quán)重和激活函數(shù)。
加重權(quán)重
首要任務(wù)是應(yīng)用權(quán)重。請注意，這里D_hat是A_hat = A + I的度矩陣，即具有強制自環(huán)的A的度矩陣。
In ［45］： W = np.matrix（［
［1， -1］，
［-1， 1］
］）
D_hat**-1 * A_hat * X * W
Out［45］： matrix（［
［ 1.， -1.］，
［ 4.， -4.］，
［ 2.， -2.］，
［ 5.， -5.］
］）
如果我們想減小輸出特征表示的維數(shù)，可以減小權(quán)重矩陣W的大小：
In ［46］： W = np.matrix（［
［1］，
［-1］
］）
D_hat**-1 * A_hat * X * W
Out［46］： matrix（［［1.］，
［4.］，
［2.］，
添加激活功能
我們選擇保留特征表示的維數(shù)并應(yīng)用ReLU激活功能。
In ［51］： W = np.matrix（［
［1， -1］，
［-1， 1］
］）
relu（D_hat**-1 * A_hat * X * W）
Out［51］： matrix（［［1.， 0.］，
［4.， 0.］，
［2.， 0.］，
［5.， 0.］］）
瞧！具有鄰接矩陣，輸入函數(shù)，權(quán)重和激活功能的完整隱藏層！
簡單樣例
最后，我們可以在真實圖上應(yīng)用圖卷積網(wǎng)絡(luò)。我將向你展示如何產(chǎn)生我們在文章開頭看到的要素表示。
扎卡里的空手道俱樂部
扎卡里（Zachary）的空手道俱樂部是一種常用的社交網(wǎng)絡(luò)，其中節(jié)點代表空手道俱樂部的成員，其邊緣相互聯(lián)系。當(dāng)扎卡里（Zachary）研究空手道俱樂部時，管理者與教練之間發(fā)生了沖突，導(dǎo)致俱樂部分裂為兩部分。下圖顯示了網(wǎng)絡(luò)的圖形表示，并且根據(jù)俱樂部的哪個部分標(biāo)記了節(jié)點。管理員和講師分別標(biāo)有“ A”和“ I”。
建立GCN
現(xiàn)在來建立圖卷積網(wǎng)絡(luò)。實際上我們不會訓(xùn)練網(wǎng)絡(luò)，只是簡單地隨機初始化，以產(chǎn)生在本文開頭看到的功能表示。我們將使用圖網(wǎng)絡(luò)networkx表示整個圖，并計算A_hat和D_hat矩陣。
from networkx import karate_club_graph， to_numpy_matrixzkc = karate_club_graph（）
order = sorted（list（zkc.nodes（）））A = to_numpy_matrix（zkc， nodelist=order）
I = np.eye（zkc.number_of_nodes（））A_hat = A + I
D_hat = np.array（np.sum（A_hat， axis=0））［0］
D_hat = np.matrix（np.diag（D_hat））
接下來，我們隨機初始化權(quán)重。
W_1 = np.random.normal（
loc=0， scale=1， size=（zkc.number_of_nodes（）， 4））
W_2 = np.random.normal（
loc=0， size=（W_1.shape［1］， 2））
堆疊GCN層：在這里，我們僅使用單位矩陣作為特征表示，即，每個節(jié)點都表示為單次熱編碼的分類變量。
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