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A directed graph with three vertices (blue circles) and three edges (black arrows). In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of ...
Examples include element-wise sum, mean or maximum. It has been demonstrated that GNNs cannot be more expressive than the Weisfeiler–Leman Graph Isomorphism Test. [29] [30] In practice, this means that there exist different graph structures (e.g., molecules with the same atoms but different bonds) that cannot be
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines).
A graph database (GDB) is a database that uses graph structures for semantic queries with nodes, edges, and properties to represent and store data. [1] A key concept of the system is the graph (or edge or relationship). The graph relates the data items in the store to a collection of nodes and edges, the edges representing the relationships ...
t. e. Exponential Random Graph Models (ERGMs) are a family of statistical models for analyzing data from social and other networks. [1][2] Examples of networks examined using ERGM include knowledge networks, [3] organizational networks, [4] colleague networks, [5] social media networks, networks of scientific development, [6] and others.
The problem of graph exploration can be seen as a variant of graph traversal. It is an online problem, meaning that the information about the graph is only revealed during the runtime of the algorithm. A common model is as follows: given a connected graph G = (V, E) with non-negative edge weights. The algorithm starts at some vertex, and knows ...
t. e. A graphical model or probabilistic graphical model (PGM) or structured probabilistic model is a probabilistic model for which a graph expresses the conditional dependence structure between random variables. They are commonly used in probability theory, statistics —particularly Bayesian statistics —and machine learning.
A graph with six vertices and seven edges. In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points) and each of the related pairs of vertices ...