Connectivity And Network Security Connectivity - 2436 Words

Connectivity and Network Security 1. Introduction In this paper, we will look into three topics: connectivity, Menger s theorem, and network flows to further understand the application of connectivity such as network systems. In graph theory, connectivity is an important topic and can be applied to many different areas. By considering the connectivity of the graph(network system map), we will be able to see clearly the problems of the graph(the system), such as low-connectivity that may lead to the vulnerability of an attack. Once we know the properties of the graph(the system), we can determine or change how the graph is or should be. 2. Connectivity A graph G is connected if for all pairs u, v ∈ G, there is a path in G from u to v. Note that it suffices for there to be a walk from u to v. [Graph Theory, p. 9] A walk in G is a sequence of vertices v0,v1,v2,...,vk, and a sequence of edges (vi, vi+1) ∈ E(G). A walk is a path if all vi are distinct. [graph_theory_notes, p. 8] Figure 1 [Graph Theory, p. 9] A (connected) component of G is a connected subgraph that is maximal by inclusion. We say G is connected if and only if it has one connected component. [Graph Theory, p. 9] Figure 2 [Graph Theory, p. 9] 2.1 Vertex connectivity A vertex cut in a connected graph G = (V,E) is a set S ⊆ V such that GS:= G[V S] has more than one connected component. A cut vertex is a vertex v such that {v} is a cut. [Graph Theory, p. 17] Notation GS= G[V S] means that, given a subsetShow MoreRelatedWifi in Corporate Environments953 Words   |  4 Pagescomplicated and requires more than just a man or woman with a dream. Success in business is now reliant on the connectivity of their business to their local area, as well as, the global market place. Wireless connectivity (Wi-Fi) in the corporate environment is making this possible and beyond possible as it improves. 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