Axiomatization of the PageRank Centrality

We propose an axiomatization of PageRank. Specifically, we introduce five simple axioms—Foreseeability, Outgoing Homogeneity, Monotonicity, Merging, and Dummy Node—and show that PageRank is the only centrality measure that satisfies all of them. Our axioms give a new conceptual and theoretical underpinnings of PageRank and show how it differs from other centralities.

A New Backward/Forward Algorithm for Weakly Meshed Distribution Systems with Distributed Generation

According to the analysis of the network topological structure, an improved backward/forward sweep algorithm was proposed. The algorithm can be applied for weakly meshed distribution systems with distributed generation (DG). The method developed an incidence matrixbranch current-bus current injection matrix. A meshed network was converted to a radial network by breaking the loops at the ending nodes of link branches. The mathematical models of DG were established as PV and PQ node. For PV nodes, this paper used a dummy node and dummy branch which inject reactive power to the specified node to maintain the specified voltage value. IEEE 33-bus test feeder was used to verify the correctness and convergence of the proposed algorithm. Moreover, the impact of both weakly meshed and DG on voltage profile and convergence was also investigated.

Path Planning Using a Hybrid Evolutionary Algorithm Based on Tree Structure Encoding

A hybrid evolutionary algorithm using scalable encoding method for path planning is proposed in this paper. The scalable representation is based on binary tree structure encoding. To solve the problem of hybrid genetic algorithm and particle swarm optimization, the “dummy node” is added into the binary trees to deal with the different lengths of representations. The experimental results show that the proposed hybrid method demonstrates using fewer turning points than traditional evolutionary algorithms to generate shorter collision-free paths for mobile robot navigation.