Introduction to the Modeling and Analysis of Complex Systems

15.2. TERMINOLOGIES OF GRAPH THEORY 299Walk A list of edges that are sequentially connected to form a continuous route on anetwork. In particular:Trail A walk that doesn’t go through any edge more than once.Path A walk that doesn’t go through any node (and therefore any edge, too)more than once.Cycle A walk that starts and ends at the same node without going through anynode more than once on its way.Subgraph Part of the graph.Connected graph A graph in which a path exists between any pair of nodes.Connected component A subgraph of a graph that is connected within itself but notconnected to the rest of the graph.Exercise 15.15See the following network and answer the following questions:361421. Represent the network in (a) an adjacency matrix, and (b) an adjacency list.2. Determine the degree for each node.3. Classify the following walks as trail, path, cycle, or other.• 6 → 3 → 2 → 4 → 2 → 1• 1 → 4 → 6 → 3 → 2• 5 → 1 → 2 → 3 → 54. Identify all fully connected three-node subgraphs (i.e., triangles).