Graafparameters

Graafparameters, in this article understood as graph parameters, are numerical descriptors that summarize the structure of a graph in graph theory and network analysis. They provide compact measures that enable comparison across graphs and help characterize the properties of networks. They can be categorized as global parameters, which describe the graph as a whole, or local parameters, which pertain to individual vertices or edges.

Commonly used graafparameters include order and size (n and m), degree sequence and distribution, density, diameter, girth, and connectivity. Global clustering coefficients, average path length, and centrality measures (betweenness, closeness, eigenvector centrality) are standard. Spectral parameters from the adjacency matrix or Laplacian, such as spectral radius and algebraic connectivity, are also common. Invariants like chromatic number, treewidth, genus, and modularity appear in more advanced contexts.

Graafparameters are computed from representations such as adjacency or incidence matrices and distance matrices. Algorithms range from BFS for distances to linear algebra for spectral properties; some parameters (for example, chromatic number and treewidth) can be computationally hard.

In research and application, graafparameters serve to classify graphs, compare networks from biology, sociology, and technology, and function as features in machine learning or network-model fitting tasks. They also underpin the study of random graph models, such as Erdős–Rényi and preferential-attachment networks, by describing their characteristic properties and enabling quantitative analysis.