Description: A quasi-embedding is a mapping of a graph into another space that preserves some, but not all, properties of the original graph. In more technical terms, it refers to a function that assigns vertices of a graph to points in a metric space, such that distances between certain vertices are maintained, although not necessarily all adjacency relationships are preserved. This means that, unlike a complete embedding, where all topological properties are preserved, in a quasi-embedding some flexibility in representation is allowed. This characteristic makes it useful in various applications where the goal is to simplify the representation of a graph without losing critical information about its structure. Quasi-embeddings are particularly relevant in the study of graphs in contexts where computational complexity is a factor, allowing researchers and professionals to work with more manageable representations of complex graphs. Furthermore, this concept relates to the theory of distance in graphs, where spatial relationships between nodes are analyzed, which can have implications in areas such as network analysis and optimization.
