New Version Revising A Mistake In Counting Degrees
Here are some statistics that we have discovered in the USAir97 Dataset which contains 332 nodes(airport) and 2126 edges(flight schedules):
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avg degree:12.81(edges_num*2/node_num）
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top10 biggest nodes by degree:[('118', 139), ('261', 118), ('255', 101), ('182', 94), ('152', 94), ('230', 87), ('166', 85), ('67', 78), ('112', 70), ('201', 68)] note that the index of the node(e.g. '118') starts from '1'
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if deliberately delete zero points in the list "degree distribution", then we get Power_Law_Omit_Zero.png, with coeff r=-1.1258094768710132 coeff b=4.394471543376857
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avg path length:2.7381247042550867(assume adjacent distances are all 1) avg path length:1849.7179(with distance amplified 9000 times using 'miles' as the measurement; note that the east-west direct distance in the US is about 2500 miles) diameter:6(assume adjacent distances are all 1)---the farthest two are node 9(1 is beginning) and 332，which belongs to Alaska and an western island near Philippines！！！ diameter:7867.5990(with distance amplified 9000 times)---the farthest two are node 68(1 is beginning) and 330, which belongs to 帕劳(在西太平洋，当时由美国托管) and 缅因州（美国东北角）
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global clustering coeff:0.6252172491625031. Currently there is not a distribution graph about (local) clustering coeff!!!
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max_coreness:26 top35 biggest nodes by coreness:['67', '112', '118', '201', '248', '166', '94', '109', '131', '147', '150', '152', '172', '176', '177', '182', '219', '230', '232', '255', '258', '261', '293', '311', '146', '159', '162', '167', '174', '179', '217', '292', '299', '301', '310']
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assortativity is -0.20787623081200443, indicating big node connects small node
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https://www.zhihu.com/question/68093386 tips about visualization tools.
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I tried to calculate NODE_BETWEENNESS myself using BFS to track possible shortest path, it could work out on small graphs, but it failed in our 332-node graph. So I switched to use the networkx package, so 'fragrant'! The largest 15 node-betweenness is: [(118, 0.20731993223098968), (8, 0.16948031947190978), (261, 0.15241740407914336), (201, 0.09384593454509225), (47, 0.09241355545314715), (182, 0.08104336166564649), (255, 0.07085473163772363), (152, 0.06916485349203222), (13, 0.06509811101956116), (67, 0.06479638197389133), (313, 0.06215761735790646), (230, 0.05421400126936584), (144, 0.048700235274616095), (166, 0.04537799052973221), (65, 0.04354882086075502)]. Also I calculated edge-betweenness. Edge-betweenness can be used to split 'communities'---See 'Girvan Newman' Algorithm. The code file is called 'betweenness.py' and I saved two dictionary-files 'node/edge_betweenness.npy'.
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A simple metrics to evaluate similarity between two nodes is to calculate their same neighbors. So I simply implemented 'jaccard_similarity.py'. Then I saved the 'jaccard_similarity_dict.npy'.