Lev Muchnik, Sinan Aral, and Sean J. Taylor, Social Influence Bias: A Randomized Experiment, Science 9 August 2013: 341 (6146), 647-651. 大众点评的餐厅评价豆瓣的电影评价购物网站的商品评价差评师的影响有多大 事先为 101281 篇网上文章随机给好评或差评，并与对照组相比 事先给好评有引导性：读者给好评的可能性提高了 32% 事先给差评没有引导性：对文章最后的评分几乎没有影响
If you have 2 large-components each occupying roughly 1/2 of the graph. How many random edges do you need to add so that the probability that the two components join into one giant component is greater than 0.9? (a) 1-5 edge additions (b) 6-10 edge additions (c) 11-15 edge additions (d) 16-20 edge additions
Your clustering coefficient: the probability that two randomly selected friends of U are friends with each other E i : no. of edges among your k i friends C i measures network’s local density: the more densely interconnected the neighborhood of node i, the higher is C i. Network clustering coefficient
Many real networks have a much higher clustering coefficient than expected for a completely random network of same no. of nodes and links High-degree nodes tend to have a smaller clustering coefficient than low-degree nodes.
Radicchi F., et al. Defining and identifying communities in networks. Proc. Natl Acad. Sci. USA 2004;101:2658-2663 The number of triangles to which a given edge belongs, divided by the number of triangles that might potentially include it, given the degrees of the adjacent nodes.
S Pajevic, D Plenz. The organization of strong links in complex networks. Nature Physics, 2012, March the relative neighbourhood overlap n C is the number of common neighbours n T is the total number of neighbouring nodes, excluding the end nodes
P(k) : The probability that the degree of a randomly selected node is k the fraction of nodes in the network with degree k
A. Clauset, C.R. Shalizi, and M.E.J. Newman, SIAM Review 51(4), 661-703 (2009) Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov–Smirnov (KS) statistic and likelihood ratios. For implementation codes, see: http://tuvalu.santafe.edu/~aaronc/powerlaws/
Given p(x), If, for any given constant a, there is a constant g(a) s.t. p(ax) = g(a) p(x) (scale-free), then there are constants C and r s.t. p(x)=C x -r (power-law).