i) start with an n by n graph G and a vertex of interest v;.
ii) pick your favorite embedding method to get n points in R^{d} (each d-dimensional vector is to be interpreted as a representation of a vertex in G);
iii) then, depending on the embedding method you use, pick a distance / dissimilarity on R^{d} (for instance, if i suspect my graph is generated from an SBM and i embed the graph using ASE / LSE i may choose either Euclidean distance for simplicity or Mahalanobis distance to exploit the assumed structure of the point in R^{d});
iv) calculate the distances between the vector corresponding to v and vectors corresponding to the other n - 1 vertices;
v) return the closest k vertices to v* says your selected distance;
i) start with an n by n graph G and a vertex of interest v;. ii) pick your favorite embedding method to get n points in R^{d} (each d-dimensional vector is to be interpreted as a representation of a vertex in G); iii) then, depending on the embedding method you use, pick a distance / dissimilarity on R^{d} (for instance, if i suspect my graph is generated from an SBM and i embed the graph using ASE / LSE i may choose either Euclidean distance for simplicity or Mahalanobis distance to exploit the assumed structure of the point in R^{d}); iv) calculate the distances between the vector corresponding to v and vectors corresponding to the other n - 1 vertices; v) return the closest k vertices to v* says your selected distance;