Afternoon saw a lightning attack on the network game of paper, the paper pointed out that lightning network is a scale-free network (scale-free network). Find a bit of science papers, write a blog when knowledge points down it.
Scale-free networks
origin
Conventional random network (e.g., model ER), although the connection is randomly set, but the number of nodes will be connected to most substantially the same, i.e., nodes in a distributed manner follow a Poisson distribution is bell-shaped, has a characteristic "Mean" . higher than the average number of connections to many or few nodes are much lower with the increase of the number of connections, the probability was rapidly decreasing exponential. therefore exponential random network known as Internet.
in 1998, AL Baraba 'si like to carry out Research on the World Wide web a drawing they had expected to find bell drawing a random network, but the results they unexpectedly found that: the World Wide web is basically a series by a handful of high connectivity of the page up, page number of connections of more than 80% . substantially the same less than 4, the total number of nodes representing nodes of less than one ten thousandth of a very small number, but more than 1000 and a random network having nodes connected to the most significant feature node has connections - "Mean" disappeared. they took such a network is called "scale-free networks."
distribution node if the scale-free networks connected logarithmic Videos in double logarithmic scale, the result will become a straight line. Thus, non-standard Network is also known as a power law distribution network
feature
Characterized in scale-free networks are most nodes in the network and only a few nodes are connected, and there is very little node connected to many nodes. The presence of such critical nodes (papers call for these nodes for the hub) == makes the network has a strong ability to withstand unexpected failure, but the face of coordinated attacks it appears fragile. After == example is the network described in the paper, as shown below, when faced with a DDoS attack against a plurality of nodes, it experienced 20 attacks, and even the entire network will be completely destroyed.
Determining scale-free networks
Distinguish whether the network is scale-free networks are not always easy. The simplest method is to observe the distribution of the logarithmic histogram. But there are many shortcomings this method itself, adding only a few of the histogram data, it may cause a lot of statistical fluctuations, so that the histogram to determine whether there is a straight line and the slope of the line there is a big problem.
There are many ways to solve the above problems. The easiest way is to expand the Chinese histogram column width, so that each sample Fang Zhurong more satisfied.
Best of both worlds different portion of the histogram approach is to use different widths of square columns. For example, the use of small data width of a square column 1, data used for a large width of the square column 5. Of course, there is no need to have to use only two kinds of different widths of the prism, can continue to increase the width of the tail shield, so that every even square pillar has a different width, the width of the pen front of a rear side of a square column column larger. With this idea the most commonly used method is the number of square columns.
Another method is to observe the power-law distribution construct cumulative distribution function.
Above with reference to the "Network Science Introduction" "scale-free networks and systems scientific significance"
