Efficient computation of the Shapley value for game-theoretic network centrality

The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley value-based centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley value-based centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two real-life examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. Fo

Tensile strength properties of polyethylene netting twines under exposure to out-door and artificial UV radiation

Photodegradation of three types of polyethylene twines namely, polyethylene fibrillated tape twine, polyethylene flat tape twine and polyethylene monofilament twines were studied by exposing them to sunlight and artificial UV radiation. The percentage residual strength varied in the samples, the monofilament with the highest residual strength followed by fibrillated tape twine and flat tape twine. A plot of the difference between the breaking strengths of the fibrillated tape twine and the mono filament twines against any given period of exposure exhibited a linear relationshi