Graph Neural Networks: Message Pass in g, Graph Convolutions, and Node Classification

Graphs have nodes and edges. GNNs learn by message passing: each node aggregates information from its neighbors. Graph convolutions are the neural network equivalent for graphs. Applications include social networks, molecular graphs, and knowledge graphs.

Message Passing

For each node v:

Aggregate neighbor messages: m_v = AGG({h_u : u ∈ neighbors(v)})
Update node: h_v_new = UPDATE(h_v, m_v)

Graph Convolution

import torch.nn as nn
from torch_geometric.nn import GCNConv
class GCN(nn.Module): def __init__(self, in_channels, hidden_channels, out_channels): super().__init__() self.conv1 = GCNConv(in_channels, hidden_channels) self.conv2 = GCNConv(hidden_channels, out_channels)
def forward(self, x, edge_index): x = self.conv1(x, edge_index) x = F.relu(x) x = self.conv2(x, edge_index) return x 

Conclusion

GNNs extend deep learning to structured graph data. Message passing is the key abstraction enabling powerful graph representations. Understanding GNNs enables modeling structured domains: molecules, social networks, knowledge graphs. Next: attention is all you need—the Transformer architecture applied to graphs.