meaning of graph embedding

Question

I read an article about community detection and it says: "the algorithm defines an embedding of the graph around the seed set.". seed set is a subgraph S of graph G. I don't understand the meaning of the sentence.

Answer 1

Basically, an embedding is a "drawing" of your graph, that respect its topological space.

A graph embedding is a representation of a graph with no intersections between edges. For example, A planar graph is a graph that has such an embedding onto the plane. The complete graph on 4 vertices (usually named $K_4$) is one example, with the following planar embedding :

A toroidal graph is a graph that has such an embedding onto a torus. For example $K_7$:

The genus of a graph is the minimum possible genus of the surface onto which it can be embedded.