Considering eigenvalues of weight matrix as graph frequencies, order the following eigenvalues from low to high frequencies.
(a) 1.0264, 3.5663, ?2.3504, ?1.4289,?0.8134
(b) 0, 0.1668, ?1.4685?0.0883j,?1.4685 + 0.0883j, 2.7703
(c)?0.3138?0.2196j, 0.6180,?1.3662?0.0847j ?1.6180, 2.6801 + 0.3042j
Also comment on the directivity and nature of edge weight (positive, real, or complex) of the
graphs.
(a) From high to low frequency: -2.3504, -1.4289, -0.8134, 1.0264, 3.5663. The graph is
undirected and the edge weights are real.
(b) From high to low frequency: -1.4685 - 0.0883j, -1.4685 + 0.0883j, 0, 0.1668, 2.7703. The
graph can be directed with real edge weights, because complex frequencies are in complex conjugate pairs.
(c) Because the complex frequencies are in complex conjugate pairs, the graph must have
some complex edge weights. From high to low frequency:
-1.6180, -1.3662 - 0.0847j, -0.3138 - 0.2196j, 0.6180, 2.6801 + 0.3042j.
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