# 流网络的引力定律

$\displaystyle{ f_{ij}\propto (T_i T_j)^{\alpha} }$

$\displaystyle{ f_{ij}\propto T_i^{\alpha}T_j^{\beta} }$

## 引力定律

$\displaystyle{ f_{ij}=\frac{Gm_im_j}{r_{ij}^2} }$

$\displaystyle{ f_{ij}=k\frac{(P_iP_j)^{\alpha}}{r_{ij}^{\beta}} }$

$\displaystyle{ f_{ij}=c (T_i T_j)^{\alpha} }$

(eq1)

$\displaystyle{ f_{ij}=c T_i^{\alpha}T_j^{\beta} }$

(eq2)

## 各种实证网络的引力定律

### 生态流网络

CrystalD 0.63 0.70 0.57 0.75 0.74
CrystalC 0.53 0.65 0.50 0.57 0.65
Chesapeake 0.68 0.84 0.62 0.77 0.85
ChesLower 0.70 0.75 0.61 0.84 0.76
ChesMiddle 0.67 0.77 0.60 0.78 0.78
ChesUpper 0.64 0.64 0.62 0.67 0.64
Narragan 0.54 0.81 0.49 0.60 0.81
Michigan 0.62 0.86 0.57 0.72 0.87
StMarks 0.68 0.74 0.76 0.56 0.75
Mondego 0.79 0.85 0.83 0.70 0.86
Cypwet 0.70 0.84 0.85 0.55 0.87
Cypdry 0.68 0.81 0.81 0.57 0.83
Gramdry 0.66 0.76 0.61 0.73 0.77
Gramwet 0.71 0.81 0.66 0.79 0.81
Mangdry 0.58 0.77 0.60 0.56 0.77
Mangwet 0.59 0.77 0.60 0.57 0.77
Baywet 0.62 0.79 0.67 0.54 0.80
Baydry 0.61 0.78 0.68 0.52 0.78
Florida 0.62 0.79 0.67 0.54 0.80

## 参考文献

1. 陈, 彦光 (2008). 分形城市系统：标度·对称·空间复杂性. 科学出版社.
2. Anderson, J. E. (2011). "The gravity model". Annual Review of Economics. 3: 133-160.
3. Zhang, Jiang (2012). "Common Patterns of Energy Flow and Biomass Distribution on Weighted Food Webs". {{cite journal}}: Cite journal requires |journal= (help); More than one of |first1= and |first= specified (help); More than one of |last1= and |last= specified (help); line feed character in |title= at position 43 (help)