The Non-trivial Correlation
Between Heterogeneity and
Disassortativity in Networks
杨丹，潘黎明，赵志丹，周涛*
[email protected]
电子科技大学•互联网科学中心•CompleX Lab
Outline
Backgrounds
Main results
Conclusions
Discussion
P2
Backgrounds-Heterogeneity
Power-law distributon
P(k )  Ck   k 
 : degree exponent
P3
Backgrounds-Disassortativity
Assortative coefficient
1
M 1  je ke  [ M 1  ( je  ke )]2
e
e 2
r
1 2 2
1
M 1  ( je  ke )  [ M 1  ( je  ke )]2
e 2
e 2
je 和 ke 分别是边e的两个端点的度，
M是网络的边数。
P4
Backgrounds-Correlation
Non-trivial bounds of assortative coefficient
with given degree distribution
analytic solution ?
P5
Outline
Backgrounds
Main results
Conclusions
Discussion
P6
Main results-Simulation
bounds
Method
edge-swap
P7
Main results
- Numerical bounds
Extend degree sequence

 1

P (k )  Ck  k
P8
Main results-Theoretical
bounds
The minimum memory of extend degree
sequence
P9
Outline
Backgrounds
Main results
Conclusions
Discussion
P10
Conclusions
We present the non-trivial correlation
heterogeneity and disassortativity .
between
Given a degree exponent, we find the approximate
analytic solution of the lower bound of disassortativity as
a function of it.
P11
Outline
Backgrounds
Main results
Conclusions
Discussion
P12
Discussion
Approximation
Limitation to the sequences
Discretization
P13
Thanks for your attention!
Question or Comment?
杨丹，潘黎明，赵志丹，周涛*
[email protected]
电子科技大学•互联网科学中心•CompleX Lab