document: Mining scale-free networks using geodesic clustering Many real-world graphs have been shown to be scale-free -- vertex degrees follow power law distributions , vertices tend to cluster , and the average length of all shortest paths is small . We present a new model for understanding scale-free networks based on multilevel geodesic approximation , using a new data structure called a multilevel mesh . Using this multilevel framework , we propose a new kind of graph clustering for data reduction of very large graph systems such as social , biological , or electronic networks . Finally , we apply our algorithms to real-world social networks and protein interaction graphs to show that they can reveal knowledge embedded in underlying graph structures . We also demonstrate how our data structures can be used to quickly answer approximate distance and shortest path queries on scale-free networks .
doc_bio_tags: O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O