Abstract
In this chapter we study the access time on random walks, i.e., the expected time for a random walk starting at a node \(v_i\) to reach a node \(v_j\), an index that can be easily calculated resorting to the powerful tools of positive systems. In particular, we argue that such an index can be the base for developing novel topological descriptors, namely access time eccentricity and diameter. While regular eccentricities and diameter are defined considering minimum paths, the indices defined in this chapter are related to random movements across the network, which may follow inefficient paths, and are thus a complementary measure to identify central and peripheral nodes and to set adequate time-to-live for the packets in a network of distributed agents, where few or no routing information is available. A simulation campaign aimed at showing the characteristics of the proposed indices concludes the chapter.
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Notes
- 1.
Each entry \(M_{ij}\) represents the probability to move from node i to node j at a given time instant.
- 2.
A graph is d-regular if the degree of each node is d.
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Oliva, G., Scala, A., Setola, R., Glielmo, L. (2017). Access Time Eccentricity and Diameter. In: Cacace, F., Farina, L., Setola, R., Germani, A. (eds) Positive Systems . POSTA 2016. Lecture Notes in Control and Information Sciences, vol 471. Springer, Cham. https://doi.org/10.1007/978-3-319-54211-9_17
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