Spike-based graph centrality measures

We derive several spike-based routines that compute or establish bounds on radial centrality measures for undirected graphs and trees without the use of matrix multiplication. These spike-based centrality measures utilize a direct embedding of graph nodes and edges into neurons and synapses, can be implemented with static synapses or plastic synapses, and rely on minimal post-processing of spike rasters. This work contributes to the growing set of graphical applications for neuromorphic hardware.

[1]  Frank Harary,et al.  Graph Theory , 2016 .

[2]  Hong Wang,et al.  Loihi: A Neuromorphic Manycore Processor with On-Chip Learning , 2018, IEEE Micro.

[3]  Kathleen E. Hamilton,et al.  Spiking spin-glass models for label propagation and community detection , 2018 .

[4]  Qiang Guo,et al.  Locating influential nodes via dynamics-sensitive centrality , 2015, Scientific Reports.

[5]  Elbert E. N. Macau,et al.  A dynamical model for community detection in complex networks , 2013, The 2013 International Joint Conference on Neural Networks (IJCNN).

[6]  Giacomo Indiveri,et al.  Memory and Information Processing in Neuromorphic Systems , 2015, Proceedings of the IEEE.

[7]  Pritish Narayanan,et al.  Neuromorphic computing using non-volatile memory , 2017 .

[8]  Kathleen E. Hamilton,et al.  Community detection with spiking neural networks for neuromorphic hardware , 2017, NCS.

[9]  Kathleen E. Hamilton,et al.  Shortest Path and Neighborhood Subgraph Extraction on a Spiking Memristive Neuromorphic Implementation , 2019, NICE '19.

[10]  Martin G. Everett,et al.  A Graph-theoretic perspective on centrality , 2006, Soc. Networks.

[11]  P. Bonacich.  Factoring and weighting approaches to status scores and clique identification , 1972 .

[12]  Ove Frank.  Using centrality modeling in network surveys , 2002, Soc. Networks.

[13]  Ojas Parekh,et al.  Spiking network algorithms for scientific computing , 2016, 2016 IEEE International Conference on Rebooting Computing (ICRC).

[14]  Jim D. Garside,et al.  SpiNNaker: A 1-W 18-Core System-on-Chip for Massively-Parallel Neural Network Simulation , 2013, IEEE Journal of Solid-State Circuits.

[15]  Andrew S. Cassidy,et al.  A million spiking-neuron integrated circuit with a scalable communication network and interface , 2014, Science.

[16]  Stephen P. Borgatti,et al.  Centrality and network flow , 2005, Soc. Networks.

[17]  Catherine D. Schuman,et al.  A Survey of Neuromorphic Computing and Neural Networks in Hardware , 2017, ArXiv.

[18]  David C. Bell,et al.  Centrality measures for disease transmission networks , 1999, Soc. Networks.

[19]  Haim Sompolinsky,et al.  Chaotic Balanced State in a Model of Cortical Circuits , 1998, Neural Computation.

[20]  Anderson Rocha,et al.  Label propagation through neuronal synchrony , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[21]  Ojas Parekh,et al.  Spiking Neural Algorithms for Markov Process Random Walk , 2018, 2018 International Joint Conference on Neural Networks (IJCNN).

[22]  Xinghuo Yu,et al.  A Maximum-Flow-Based Complex Network Approach for Power System Vulnerability Analysis , 2013, IEEE Transactions on Industrial Informatics.

[23]  G. Ermentrout,et al.  Synchrony, stability, and firing patterns in pulse-coupled oscillators , 2002 .

[24]  Yong Deng,et al.  Identifying influential spreaders by weight degree centrality in complex networks , 2016 .

[25]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[26]  H. Sompolinsky,et al.  Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity , 1996, Science.

[27]  Zhoujun Li,et al.  Negative Influence Minimizing by Blocking Nodes in Social Networks , 2013, AAAI.

[28]  L. Freeman.  Centrality in social networks conceptual clarification , 1978 .

[29]  D. Sade,et al.  Sociometrics of Macaca Mulatta III: n-path centrality in grooming networks , 1989 .

[30]  Romain Brette,et al.  Neuroinformatics Original Research Article Brian: a Simulator for Spiking Neural Networks in Python , 2022 .

[31]  Aric Hagberg,et al.  Exploring Network Structure, Dynamics, and Function using NetworkX , 2008, Proceedings of the Python in Science Conference.

[32]  Catherine D. Schuman,et al.  Simulating and Estimating the Behavior of a Neuromorphic Co-Processor , 2017 .

[33]  Kathleen E. Hamilton,et al.  Non-Neural Network Applications for Spiking Neuromorphic Hardware , 2013 .