Cycle Graphs Sample Clauses

Cycle Graphs. A cycle graph Cn (also referred to by n- cycle, n-ring, or even circle) is an undirected graph such that V = {v1, . . . , vn} xiThe reason why we cannot fully see Xxxxxxxx’x algorithms as a linear voting model (see Section 2.4.3) is because the probability of an agent maintaining their state depends on their previous interaction, and thus might change over time, whereas linear voting models assume probabilities are constant. and E = {(v1, v2), (v2, v3), . . . , (vn, v1)}. If n is odd, we will say Cn is an odd cy- cle. Otherwise, Cn is an even cycle. We say we move clockwise if we consider the sequence (v1, v2, . . . , vn, v1, . . . ). It is considering this sequence that we add or subtract indexes of nodes in a cycle. For example, in the context of C20, v15+7 = v2. We also make reference to odd nodes (or odd positioned nodes) in a cycle, i.e., the set {vk | k is odd}. Analogously, we refer to even nodes (or even po- sitioned nodes). When cycles are depicted in figures, unless stated otherwise, v1 will be the top-most vertex (with indexes increasing clockwise) (see Remark 2.4.3).