The Small World Phenomenn An Algorithmic Perspective小世界现象，算法的角度.pptVIP

The Small World Phenomenon: An Algorithmic Perspective Jon Kleinberg Oh, it’s such a small world!! Milgram (1967, 69) – performed an empirical validation of the small world concept in sociology. Previous work- Pool and Kochen model 2 people at random connected with k intermediaries. Assumes synthetic, homogenous structure. Rapaport and Horvath – empirical study on school friendships. Asymmetric nets and Universe is small. Packet sent by a randomly chosen source to a random target. Mean chain length = 5.2 Variables of geographic proximity, profession and sex Funneling of chains by certain individuals Small world! Small world! White (1970) – tries fitting a simple model to Milgram’s work. Gives hints to future work Killworth Bernard (1979) – Reverse SW To understand social network structure, factors that influence the choice of acquaintance, the out-degree of people. Results: Generation of contacts not purely random. Large number of contacts for local targets; few contacts for non-local targets. The size of geographical area that a single contact is responsible for decreases as a function of the distance of the target from starter. Most choices based on cues of occupation and geographic location. Small Worlds Everywhere Watts and Strogatz (1998) Very small number of long range contacts needed to decrease path lengths without much reduction in cliquishness. Long range contact picked uniformly at random (u.a.r) Small world networks in 3 different areas esp. spread of infectious disease. Probabilistic reach. No specific destinations. Doesn’t require knowledge of paths and no active path selection. Barabasi et al.(1999) – diameter of the WWW Power-law distribution; Logarithmic diameter. Need for search engines to intelligently pick links Two Important Properties of Small World Networks Low average hop count High clustering coefficient Additionally, may be searchable on the basis of local information Enter Kleinberg… Two issues of concern in small-world networks: P