Multi-relational Graphs

Multi-relational graphs extend traditional graphs by allowing different types of edges to represent different relationships between nodes. Each edge is associated with a specific edge type or relation [Tex]\tau[/Tex], denoted as (u, \tau, v) \in E, where u and v are nodes connected by the edge of type [Tex]\tau[/Tex]. The graph can be represented by an adjacency tensor A of shape [Tex]|V|\times|R|\times|V|[/Tex], where ∣R∣ is the number of distinct edge types or relations.

Heterogenous Graph

• Heterogeneous graphs are a subset of multi-relational graphs where nodes and edges can have different types or categories.
• Nodes in a heterogeneous graph may represent different types of entities (e.g., users, products, events), and edges may represent different types of relationships or interactions between these entities.
• For example, in a social network, nodes could represent users, pages, and events, while edges could represent friendships, likes, and attendances.
• Heterogeneous graphs provide a flexible framework for modeling complex relationships and interactions in various domains.

Multiplex Graphs

• Multiplex graphs are another subset of multi-relational graphs where different layers or “layers” of edges exist, each representing a distinct relationship between nodes.
• Unlike heterogeneous graphs, multiplex graphs typically have homogeneous nodes (i.e., all nodes belong to the same type), but different layers of edges capture different types of interactions between these nodes.
• For example, in a transportation network, one layer of edges could represent road connections, while another layer could represent railway connections.
• Multiplex graphs are useful for modeling systems with multiple interaction modalities or networks with diverse edge types.

In this article we are going to learn about Graph representation in Machine Learning (ML). Graph is basically a data structure which provide a mathematical model of representing information by the collection of nodes and edges connecting them. It is used in machine learning to solve the problem of real world with an ease and implement the algorithm accordingly. Hence, graph representation is an essential part of study of Machine learning. In this article, we are going to discuss graph theory, graph representation learning and more.