A Method for Generating Sparse Undirected Connected Random Graphs

Abstract

The invention discloses a method for generating a sparse undirected connected random graph, and researches on the generation problem of a connected and sparse random graph belonging to an undirected graph in the condition of the given average degree d and the vortex number n. The method aims at the generation problem of the random graph, and proposes a DSCA (Dual Stage Construction Algorithm); a tree comprising n vortexes is firstly and randomly generated, and then a certain number of edges are randomly added on the basis of the tree, wherein the number of the edges meets the requirements of the given average degree. According to the method for generating the sparse undirected connected random graph disclosed by the invention, a support tree is firstly and randomly generated, and then a certain number of the edges are randomly added on the basis of the support tree, thereby obtaining the undirected connected random graph. According to the method disclosed by the invention, the problem of rapid and random generation of the sparse undirected connected graph is solved.

Description

technical field [0001] The invention relates to a graph generation method. In particular, it relates to a method for generating sparse undirected connected random graphs. Background technique [0002] A network is a system composed of a series of related individuals. Many systems in the real world can be represented by networks, such as communication networks, social networks, and power networks. The network can be represented by N=(V, E, C, W), where V represents the set of vertices in N, E represents the set of edges in N, C represents the weight of edges in N, and W represents The weight of the vertex. When C and W are not considered, G=(V,E) is called a graph. Taking the power grid as an example, generators (power points) and substations (load points) can be regarded as vertices in the power network, power lines are edges in the power network, edge weights are the impedance of power lines, etc., point weights are loads power or generator output, etc. Considering tha...

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Problems solved by technology

The algorithm can theoretically guarantee the connectivity of the generated random graph, and can accurately control the AD of the random graph. However, in each step of the edge removal process, it is necessary to determine which edges in the current graph are cutting edges, and the calculation of the cutting edge The time complexity is O(n 3 ), so the overall time complexity of the algorithm is O(n 4 ), when n is large, such as thousands or even tens of thousands of vertices in the high-voltage transmission network, the algorithm cannot complete the calculation in a limited time

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