Cartography of the farcaster network
- Started by taking edge/node data from nounderline/farcaster-social-graph. 500 users, 36,348 edges.
- Graph equivalent for the laplace operator,
$\nabla^2$ . $$ L = D - A $$ where -
$D$ is the degree of the vertex.$D_{in}$ ,$D_{out}$ and therefore$L_{in}$ ,$L_{out}$ are different. -
$A$ adjacency matrix, symmetric for undirected graphs.
- Eigenvector/values of laplacian matrix can be used for spectral clustering. To create a K-dimensional embedding:
- Compute Laplacian matrix of graph, potentially normalise.
- Compute K smallest eigenvalues, use associated K eigenvectors to create a
$(n, k)$ embedding matrix. - Clustering via traditional clustering techniques for dense
$(n, k)$ matrices, e.g. k nearest neighbours.