| “Bridge” and “local bridge” are important concepts in the area of social network analysis.In this Master thesis,I generalize the notions of “bridge” and “local bridge” to ternary relations between two sets of points A,B and a set of edge R in networks,i.e.,any path from A to B(of length ≤ n)passes through some edge in R.It turns out that these ternary relations are closely related to other notions like robustness in network analysis and betweenness in graph theory,etc.I proposed a logical system LB that enables us to reason about these ternary relations and proved its soundness,completeness and decidability.Some problems about the expressivity of LB are also considered in this article.In the end,I try to extend the logical framework to directed networks and weighted networks.It is suggested that,in spite of the smoothness of extending the current framework to directed graph,the case of weighted graph is instead nontrivial and still an open problem. |
