China
Africa
Explore chapters and articles related to this topic
Spectrum Fragmentation Management Approaches Considering Non-defragmentation
Published in Bijoy Chand Chatterjee, Eiji Oki, Elastic Optical Networks: Fundamentals, Design, Control, and Management, 2020
Bijoy Chand Chatterjee, Eiji Oki
Multigraph approach [175, 176] was introduced to suppress the bandwidth fragmentation and improve the traffic admissibility. In this approach, N – b + 1 graphs are generated, where b is the number of required slots for each request and N is the total number of slots between two nodes. These graphs are produced by considering each edge of a multigraph. Each multigraph is allowed to have multiple edges (also called parallel edges) that have the same end nodes. Thus, two vertices may be connected by more than one edge in a multigraph. The edges of a multigraph are typically mapped onto a single edge of each generated graph whose cost is determined by applying a specific cost function, which considers all b edges. To select the best path, a shortest path algorithm is executed for each generated graph.
Graph Theory
Published in Rowan Garnier, John Taylor, Discrete Mathematics, 2020
Unfortunately there are many variations on the definition of a graph. Some authors use a definition which excludes the possibility of multiple edges in their graphs; that is, several edges connecting the same pair of vertices. Other definitions exclude the possibility of loops—edges which join a vertex to itself. We shall call a graph which satisfies both these restrictions—that it has no loops or multiple edges—a simple graph †. The terminology of graph theory is distinctly non-standard. When consulting other texts you are strongly advised to check very carefully the author's definitions and terminology.
A general framework for NCS modeling
Published in Longo Stefano, Tingli Su, Herrmann Guido, Barber Phil, Optimal and Robust Scheduling for Networked Control Systems, 2018
Longo Stefano, Tingli Su, Herrmann Guido, Barber Phil
Instead of a single communication network N, let us assume now that there are n ‘parallel’ networks which may or may not share some or all the nodes. For instance, a wireless NCS where two distinct frequency bands are used for communication is an example of an NCS with two parallel networks. This can be represented as a multigraph. A multigraph is a graph where multiple edges (i.e. edges having the same end vertices) are permitted. Figure 3.7 shows an
A new approach to software vulnerability detection based on CPG analysis
Published in Cogent Engineering, 2023
CPG was introduced by Yamaguchi et al. (2014). Accordingly, CPG combines 3 code representation graphs (namely AST (Yamaguchi et al., 2012), CFG (Gascon et al., (2013), PDG (Ferrante et al., 1989) into a common data structure. A CPG graph consists of the following main components: Nodes and node types. Nodes represent the program structure. It includes low-level language constructs such as methods, variables, control structures, but it also has higher-level constructs such as HTTP endpoints or findings. Each node has a type that specifies the program structure type represented by the node. For example, a node with type METHOD represents a method while a node with type LOCAL represents defining a local variable.Labeled edges. Relationships between program structures are represented through edges between respective nodes. For example, to represent a method that contains a local variable, we can create an edge with the label CONTAINS from a node METHOD to the local node. By using labeled edges, we can represent many relationship types in the same graph. Multiple edges can exist between two identical nodes.Key-value pairs. Nodes contain key-value feature pairs where the valid keys depend on the node type. For example, a method has at least one name and one signature, while a local declaration has at least one name and type of the declared variable.
A Method for Information Security Analysis Using Information Graphs
Published in Cybernetics and Systems, 2022
We do not create multiple edges, only one multi-edge between adjacent vertices of the graph. Instead of adding more edges, we add their information classifiers to the set of KLI(e). There are as many added classifiers as multiple edges with different classifiers with the addition operation. We do the same for its adjacent vertices. We will call such an operation edge and vertex overloading.