Spectral Ranking in Complex Networks Using Memristor Crossbars

Various centrality measures have been proposed to identify the influence of each node in a complex network. Among the most popular ranking metrics, spectral measures stand out from the crowd. They rely on the computation of the dominant eigenvector of suitable matrices related to the graph: EigenCentrality, PageRank, Hyperlink Induced Topic Search (HITS) and Stochastic Approach for Link-Structure Analysis (SALSA). The simplest algorithm used to solve this linear algebra computation is the Power Method. It consists of multiple Matrix-Vector Multiplications (MVMs) and a normalization step to avoid divergent behaviours. In this work, we present an analog circuit used to accelerate the Power Iteration algorithm including current-mode termination for the memristor crossbars and a normalization circuit. The normalization step together with the feedback loop of the complete circuit ensure stability and convergence of the dominant eigenvector. We implement a transistor level peripheral circuitry around the memristor crossbar and take non-idealities such as wire parasitics, source driver resistance and finite memristor precision into account. We compute the different spectral centralities to demonstrate the performance of the system. We compare our results to the ones coming from the conventional digital computers and observe significant energy savings while maintaining a competitive accuracy.