So we have seen how to compute degree histograms of a graph. While degree histograms are useful to characterize a graph, it is usually a means to an end. It's a known practice in statistics to compute a mathematical expression for a statistical distribution Using histograms. For graphs, we often look for a function to describe the degree distribution. But this is expressed as a distribution of the probability that a random vertex will have exactly k neighbors. Now, this problem has been investigated by many. One popular, well known model, is a Power Law. A graph follows a Power Law if, the best probability is given by k, erased to a negative exponent called alpha. The value of alpha, for many practical networks, is between two and three. More recently, people have suggested other distributions that look like the power law graph. One of them is a log-normal graph. Here, the logarithm of k has a Gaussian distribution. So this log-normal distribution seems to have the better fit to natural graphs that are observed. So, why are power law graphs important? Interestingly, many very, very different real life graphs in the world seem to follow the power law. If a graph does follow the power law, it would have one large connected component with a very high proportion of notes connected to it In a power law graph, most nodes have a low degree and some nodes will be disconnected. The low degree nodes belong to a very dense sub graphs and those sub graphs are connected to each other through hubs. In the center of the graph has a high density, power law graphs can be difficult to compute with. For example, the shortest path algorithm operating in the dense part will possibly be very inefficient, not because of the size of the network, but because there are too many paths to explore inside the denser pieces. The more interesting reason why people study power-law graphs is because power-law graphs are supposed to be robust. So in nature, all biological networks show power-law graphs because It gives you a high rate of redundancy against failure and attacks.