Network Dynamics

Degree Matrix

The Degree Matrix is a square matrix that provides insights into the connectivity of nodes in a graph. For directed graphs, it reflects the number of incoming and outgoing edges for each node, while for undirected graphs, it represents the number of edges incident to each node.

Laplacian Matrix

The Laplacian Matrix is a square matrix derived from the adjacency matrix and degree matrix of a graph. It is instrumental in analyzing various properties of the graph, such as connectedness, the count of spanning trees, and other spectral characteristics.

Transition Matrix

The Transition Matrix is commonly used in the study of Markov Chains and stochastic processes. Within the context of a graph, it denotes the probabilities of transitioning from one node to another, often based on the edge weights or predetermined criteria. This matrix finds applications in various fields such as network analysis, machine learning, and optimization.