# Article

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Keywords:
algebraic connectivity; Fiedler vector
Summary:
Let \$G\$ be a \$k\$-connected graph with \$k \ge 2\$. A hinge is a subset of \$k\$ vertices whose deletion from \$G\$ yields a disconnected graph. We consider the algebraic connectivity and Fiedler vectors of such graphs, paying special attention to the signs of the entries in Fiedler vectors corresponding to vertices in a hinge, and to vertices in the connected components at a hinge. The results extend those in Fiedler's papers Algebraic connectivity of graphs (1973), A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory (1975), and Kirkland and Fallat's paper Perron Components and Algebraic Connectivity for Weighted Graphs (1998).
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