6.4.4 Graph theory

Problem: Using the vertex adjacency matrix, construct a graph diagram. Build flat layout. Create an adjacency matrix of the edges and an incidence matrix. Find the eccentricities of the vertices, the radius and diameter of the graph, peripheral, central vertices, diametrical chains. Find all cycles. Construct a cyclomatic matrix. Color the graph. \[ \left(\begin{array}{lllll} 0 & 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 & 0 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 1 & 1 & 0 \end{array}\right) . \]