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Research and Application of Network Energy on Mixed Graphs
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    Abstract:

    The energy of the traditional mixed graph is obtained by calculating the eigenvalues of the matrix in the form of a square matrix,and it is difficult to be extended to large-scale mixed graphs. In response to this problem, this paper applies the network dimension to the mixed graph, and proposes the network energy of the mixed graph, thus the network energy is extended from the undirected graph and the directed graph to the mixed graph. The network energy of a mixed graph can be obtained by the number of nodes and the number of directed and undirected edges of the mixed graph. At the same time,several upper and lower limits of the network energy of the mixed graph are given. Comparied with the Hermitian energy of mixed graph and the network energy of directed and undirected graphs, some important properties of the proposed network energy of the mixed graph are analyzed. The internal relationships among undirected graph, directed graph and mixed graph are also demonstrated.

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  • Received:
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  • Online: June 25,2021
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