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— In this paper, we consider the problem of relative localization in a network of sensors, according to the formulation of Barooah and Hespanha. We introduce a distributed algorithm for its solution, and we study the algorithm performance by evaluating a suitable performance metric as a function of the network eigenvalues. Remarkably, the performance… (More)

Important applications in robotic and sensor networks require distributed algorithms to solve the so-called relative localization problem: a node-indexed vector has to be reconstructed from measurements of differences between neighbor nodes. In a recent note, we have studied the estimation error of a popular gradient descent algorithm showing that the mean… (More)

The average effective resistance of a graph is a relevant performance index in many applications, including distributed estimation and control of network systems. In this paper, we study how the average resistance depends on the graph topology and specifically on the dimension of the graph. We concentrate on d-dimensional toroidal grids and we exploit the… (More)

In our recent paper W.S. Rossi, P. Frasca and F. Fagnani, " Average resistance of toroidal graphs " , SIAM Journal on Control and Optimization , 53(4):2541–2557, 2015, we studied how the average resistances of d-dimensional toroidal grids depend on the graph topology and on the dimension of the graph. Our results were based on the connection between… (More)

In this paper we elaborate upon a measure of node influence in social networks, which was recently proposed by Vassio et al., IEEE Trans. Control Netw. Syst., 2014. This measure quantifies the ability of the node to sway the average opinion of the network. Following the approach by Vassio et al., we describe and study a distributed message passing algorithm… (More)

The spread of new beliefs, behaviors, conventions, norms, and technologies in social and economic networks are often driven by cascading mechanisms, and so are contagion dynamics in financial networks. Global behaviors generally emerge from the interplay between the structure of the interconnection topology and the local agents' interactions. We focus on… (More)

The average effective resistance of a graph can be computed as a function of its eigenvalues. Using this formula and focusing on toroidal d-dimensional graphs, we study the role of the network topology and specifically of the graph dimension in determining the resistance. Considering sequences of graphs of increasing size, we study the asymptotical behavior… (More)

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