A continuous-time quantum walk (CTQW) on a graph , where is the set of vertices (nodes) and is the set of edges connecting the nodes, is defined as follows: Let be the adjacency matrix of . The continuous-time quantum walk on the graph is then defined by the unitary matrix , where is the imaginary unit and . The probability of a walk starting at vertex ending up at vertex at time is given by . The size and color of vertex represent when the system is measured.