# The harmonic influence in social networks and its distributed computation by message passing

Paolo Frasca
(CNRS, Gipsa-lab, Grenoble)

When |
Jul 03, 2018
from 01:30 PM to 02:30 PM |
---|---|

Where | room M7.101 |

Attendees |
Paolo Frasca |

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An important issue in the study of dynamical processes on networks is the identification of the most influential nodes, i.e. those with the higher ability to drive the others towards a desired state. The harmonic influence is a measure that quantifies the ability of a leader node to alter the average opinion of a social influence network with linear interactions, acting against an adversary field node. Its computation is equivalent to solve a discrete Dirichlet problem associated to a grounded Laplacian for every node. The harmonic influence can be approximated by a distributed message-passing algorithm, inspired by an analogy between electrical and social networks on tree graphs. The algorithm is guaranteed to convergence on any connected graph with symmetric Laplacian. Our simulations show that when the network has a larger number of cycles, the algorithm becomes slower and less accurate, but nevertheless provides a useful approximation.