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Which of the two representations, adjacency matrix or adjacency list, is better Well, it depends on the relationship between |V |, the number of nodes in the graph, and |E|, the number of edges |E| can be as small as |V | (if it gets much smaller, then the graph degenerates for example, has isolated vertices), or as large as |V | 2 (when all possible edges are present) When |E| is close to the upper limit of this range, we call the graph dense At the other extreme, if |E| is close to |V |, the graph is sparse As we shall see in this chapter and the next two chapters, exactly where |E| lies in this range is usually a crucial factor in selecting the right graph algorithm Or, for that matter, in selecting the graph representation If it is the World Wide Web graph that we wish to store in computer memory, we should think twice before using an adjacency matrix: at the time of writing, search engines know of about eight billion vertices of this graph, and hence the adjacency matrix would take up dozens of millions of terabits Again at the time we write these lines, it is not clear that there is enough computer memory in the whole world to achieve this (And waiting a few years until there is enough memory is unwise: the Web will grow too and will probably grow faster) With adjacency lists, representing the World Wide Web becomes feasible: there are only a few dozen billion hyperlinks in the Web, and each will occupy a few bytes in the adjacency list You can carry a device that stores the result, a terabyte or two, in your pocket (it may soon t in your earring, but by that time the Web will have grown too) The reason why adjacency lists are so much more effective in the case of the World Wide Web is that the Web is very sparse: the average Web page has hyperlinks to only about half a dozen other pages, out of the billions of possibilities.

fueled by the fear, greed, and hope of millions of market participants So it should not be surprising that the market indicators in this chapter are used to monitor what the crowd is feeling These indicators are perhaps the easiest to read and understand, but they can give you the most revealing clues, especially at market extremes Knowing when the crowds are panicked or overconfident is essential if you are going to enter the market The stock market is psychological warfare, and you d better know what others are thinking before you enter The following indicators are commonly referred to as sentiment indicators because they monitor the sentiment, or psychology, of the market And as you ll soon find out, it s an Alice in Wonderland kind of world, where up is down and down is up Traders and investors closely follow the first indicator, the AAII Sentiment Survey

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When you add two fractions using the above method, the result might not be in lowest terms As a final step in the addition of two fractions, you can reduce the result to lowest terms But you don t always have to By now you must wonder, Does it matter whether or not a fraction is in lowest terms The answer is, It depends If you want to express a fraction in the simplest or most elegant possible way, you should reduce it But you will sometimes come across situations where it s better to put a fraction, ratio, or proportion in a form other than lowest terms

Depth- rst search is a surprisingly versatile linear-time procedure that reveals a wealth of information about a graph The most basic question it addresses is, What parts of the graph are reachable from a given vertex To understand this task, try putting yourself in the position of a computer that has just been given a new graph, say in the form of an adjacency list This representation offers just one basic operation: nding the neighbors of a vertex With only this primitive, the reachability problem is rather like exploring a labyrinth (Figure 32) You start walking from a xed place 85

Suppose you want to describe how many people in Country X have green eyes, per 100,000 population You might discover that one out of every 10 people has green eyes You could say that 1/10 of the people have green eyes, or the ratio of people with green eyes to all the people in Country X is 1:10 But if you use 100,000 population as a basis, you ll have to say that the proportion of people with green eyes is 10,000 per 100,000 population in Country X That s not even close to the lowest form, but it conveys the intended meaning better In pure theory, it doesn t matter if a fraction, ratio, or proportion is in lowest terms or not These days, nearly everyone uses computers in complicated calculations, and the machines don t care about lowest terms You can input the numbers as they are, and the computer will output the data in any form you want

Name: American Association of Individual Investors (AAII) Where to find: wwwaaiicom/sentimentsurvey, Barron s, Forbes, and other financial periodicals

Here s a challenge!

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