András Telcs

Sub-Gaussian estimates of heat kernels on infinite graphs

We prove that a two-sided sub-Gaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.

Lobby index in networks

We propose a new node centrality measure in networks, the lobby index, which is inspired by Hirsch’s h-index. It is shown that in scale-free networks with exponent α the distribution of the l-index has power tail with exponent α(α+1). Properties of the l-index and extensions are discussed.

Adaptive sink mobility in event-driven multi-hop wireless sensor networks

Optimizing energy consumption in wireless sensor networks is of paramount importance. There is a recent trend to deal with this problem by introducing mobile elements (sensors or sink nodes) in the network. The majority of these approaches assume time-driven scenarios and/or single-hop communication between participating nodes. However, there are several real-life applications for which an event-based and multi-hop operation is more appropriate. In this paper we propose to adaptively move the sink node inside the covered region, according to the evolution of current events, so as to minimize the energy consumption incurred by the multi-hop transmission of the event-related data. Both analytical and simulation results are given for two optimization strategies: minimizing the overall energy consumption, and minimizing the maximum load on a specific sensor respectively. We show that by adaptively moving the sink, significant power saving can be achieved, prolonging the lifetime of the network.

Random Walks on graphs, electric networks and fractals

SummaryThis paper is devoted to the problem of the nearest, neighbour Random Walk on infinite graphs. We investigate the RW Xn started from a fixed vertex X0=x∈V of the graph G=(V, E) and the expected value of the first exit time TN from the N-ball BN in G. It will be shown that if G is sufficiently “regular” then

Hirsch-type indices for characterizing networks

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