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Graph theory concepts and definitions used in image processing and analysis
Published in Olivier Lézoray, Leo Grady, Image Processing and Analysis with Graphs, 2012
The advantage of adjacency lists over matrix representations is less memory usage. Indeed, a full incidence matrix requires O(|V|×|ℰ|) memory, and a full adjacency matrix requires O(|V|2) memory. However, sparse graphs can take advantage of sparse matrix representations for a much more efficient storage.
Mission Framework
Published in Yasmina Bestaoui Sebbane, Intelligent Autonomy of Uavs, 2018
The adjacency matrix A $ \mathbf A $ of an undirected graph is its own transpose A=AT $ A = A^T $ . An adjacency matrix can also represent a weighted graph. When the graph is dense, an adjacency matrix representation is preferred. When the graph is sparse, the adjacency list is preferred.
Introduction to graph theory
Published in Karthik Raman, An Introduction to Computational Systems Biology, 2021
The adjacency list maintains a list of all the nodes adjacent to a given node in the graph. More efficient representations of the adjacency list can be achieved by using adjacency maps. The adjacency list has |V| rows, with each row having di entries (listed against node i), where di is the number of neighbours of the ith node. Figure 2.5d illustrates the adjacency list for the directed graph in Figure 2.5b.
Anomaly detection in large-scale networks: A state-space decision process
Published in Journal of Quality Technology, 2021
Abdullah Alghuried, Ramin Moghaddass
All of the above variables for large-scale sparse networks can be determined from the adjacency lists with labeled nodes, which are known as the most common representations for sparse graphs. For node i, adjacency list Ai is defined as an array A, which contains all the vertices that are adjacent to any vertex i. Since most real-world networks have a large structure, and thus, have large sparse graphs, representing the edges using adjacency lists for such systems requires less storage space.