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We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the smallest possible average distance. In contrast, there are many graphs with the same minimum average distance , ignoring… (More)

- Dionysios Barmpoutis, Richard M. Murray
- ArXiv
- 2010

Crosstalk is defined as the set of unwanted interactions among the different entities of a network. Crosstalk is present in various degrees in every system where information is transmitted through a means that is accessible by all the individual units of the network. Using concepts from graph theory, we introduce a quantifiable measure for sensitivity to… (More)

- Dionysios Barmpoutis, Richard M. Murray
- ArXiv
- 2011

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness cen-trality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks.

We describe how noise propagates through a network by calculating the variance of the outputs. Using stochastic calculus and dynam-ical systems theory, we study the network topologies that accentuate or alleviate the effect of random variance in the network for both directed and undirected graphs. Given a linear tree network, the variance in the output is a… (More)

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