Abstract
Network connectivity is an important factor in data transmission, information sharing, and network defense, and it is a crucial indicator which determines the performance of a network. When a network node or channel contains uncertainties in both positive and negative aspects, the entire network can be modeled with bipolar fuzzy graphs. This paper analyzes the influence of each vertex on the connectivity of the entire network through the definition of the connected state on the bipolar fuzzy graph. The solid results are given, and the new concepts are applied in campus network connectivity analysis. This approach helps to analyze the hidden dangers of the bipolar network, find the weaknesses in the connection, and prevent network attacks in advance.
Highlights
In information science, the connectivity of the network and the connected state of each vertex determine the efficiency of the entire network and the corresponding algorithm
The positive uncertainty corresponds to the positive membership function value, and the negative uncertainty corresponds to the negative membership function value
It inspires us to extend these concepts to more fuzzy settings, and in this work, we focus on bipolar fuzzy setting. e contributions of this work are three-fold: first, we introduce the bipolar connectivity status of each vertex and entire network; some theoretical results are inferred in light of fuzzy theory and graph theory; and the given tricks are used in campus network connectivity analysis which aims to prevent network attacks in advance
Summary
The connectivity of the network and the connected state of each vertex determine the efficiency of the entire network and the corresponding algorithm. The positive uncertainty corresponds to the positive membership function value, and the negative uncertainty corresponds to the negative membership function value In this setting, the network model becomes a bipolar fuzzy graph, and different types of uncertainties can use different membership functions and determine various frameworks of the bipolar fuzzy graph. Several works contribute to bipolar fuzzy sets and bipolar fuzzy graphs from the perspective of theory and application. E contributions of this work are three-fold: first, we introduce the bipolar connectivity status of each vertex and entire network; some theoretical results are inferred in light of fuzzy theory and graph theory; and the given tricks are used in campus network connectivity analysis which aims to prevent network attacks in advance. E organization of the rest sections are as follows: we present the basic existing concepts on bipolar fuzzy graph in Section 2; new definitions, theoretical results, and proofs are determined in Section 3; a numerical experiment is manifested in Section 4 which simulates university campus network; and the conclusion and remarks are given in the last section
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