# A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications - Author(s): Hongyun Cai, Vincent W. Zheng, and Kevin Chen-Chuan Chang - Date: 2018 - Publication: # IEEE Transactions on Knowledge and Data Engineering - [Link](https://ieeexplore.ieee.org/abstract/document/8294302) --- ## The graph embedding problem > Graph embeddings problems typically try to represent a graph as a low dimensional vector while preserving the graph structure/information. Graph embeddings problems are generally related to two types of problems: 1. *Graph analytics*: tries to mine useful information from graph data 2. *Representation learning*: obtains data representations in an attempt to extract useful information when building classifiers or other predictors **Graph embedding lies in the overlap of the two problems and focuses on *learning the low dimensional representations.*** Challenges of graph embedding depend on the problem setting, which depends on the type of graph input you have and the type of graph output you desire. ### Definitions An example graph. ![[graphEmbeddings_Review1.png]] A **graph** $G = (V,E)$, where $v \in V$ is a node and $e \in E$ is and edge. The authors make distinctions between the following types of graphs: - *Homogenous graph*: All nodes belong to a single type of node class and all edges belong to a single type of edge class - *Heterogenous graph*: A graph where there are either gt; 1$ node type or gt; 1$ edge type - *Knowledge graph*: A directed graph whose nodes are *entities* and edges are *subject-property-object* triple facts. Specifically, each edge forms a *(head entity, relation, tail entity)* — denoted as lt;h,r,t>$ — which indicates a relationship $r$ from entity $h$ to entity $t$ (see example below). ![[graphEmbedding_Review2.png]] > A knowledge graph representation of the above would contain two triplets: lt;Alice,isFriendOf,Bob>$ and lt;Bob,isSupervisorOf,Chris>$ **First-order proximity**: the weight of an edge — $e_{ij}$ — between node $v_i$ and $v_j$; denoted as $s_{ij}^{(1)}$. The first order proximity between --- #### Related [[graph_embeddings]]