Abstract-In this paper, we redefine the Graph Fourier Transform (GFT) under the DSPG framework. We consider the Jordan eigenvectors of the directed Laplacian as graph harmonics and the corresponding eigenvalues as the graph frequencies. For this purpose, we propose a shift operator based on the directed Laplacian of a graph. Based on our shift operator, we then define total variation of graph signals, which is used in frequency ordering. We achieve natural frequency ordering and interpretation via the proposed definition of GFT. Moreover, we show that our proposed shift operator makes the LSI filters under DSPG to become polynomial in the directed Laplacian.

No abstract

No abstract

No abstract

No abstract

No abstract

Many regular networks suffer from significant network delay due to large end-to-end hop distance among source nodes and destination nodes in the network. However, the presence of a few long-ranged links transforms a regular network to a small-world network, and thus, optimizes network delay by minimizing end-to-end hop distance. In this paper, we study various deterministic long-ranged link addition strategies (e.g., based on average path length, average edge length, betweenness centrality, closeness centrality, and closeness centrality disparity) to incorporate small-world characteristics as well as to optimize average network delay of the network. Moreover, we analyze time complexity to assess the efficiency of each strategy in detail. We observe, in an N node network, that deterministic long-ranged link addition by closeness centrality disparity (CCD) strategy is only O(N 2 × log N ) time complex compared to other optimal long-ranged link addition strategies which take O(N 4 × log N ) time to achieve similar performance in the context of average network delay.Index Terms-Regular network, small-world network, average network delay, closeness centrality, closeness centrality disparity.

No abstract