Limits...
Emergence of disassortative mixing from pruning nodes in growing scale-free networks.

Wang SJ, Wang Z, Jin T, Boccaletti S - Sci Rep (2014)

Bottom Line: Disassortative mixing is ubiquitously found in technological and biological networks, while the corresponding interpretation of its origin remains almost virgin.We here give evidence that pruning the largest-degree nodes of a growing scale-free network has the effect of decreasing the degree correlation coefficient in a controllable and tunable way, while keeping both the trait of a power-law degree distribution and the main properties of network's resilience and robustness under failures or attacks.We support our claims via numerical results and mathematical analysis, and we propose a generative model for disassortative growing scale-free networks.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Shaanxi Normal University, Xi'An City, ShaanXi Province, China.

ABSTRACT
Disassortative mixing is ubiquitously found in technological and biological networks, while the corresponding interpretation of its origin remains almost virgin. We here give evidence that pruning the largest-degree nodes of a growing scale-free network has the effect of decreasing the degree correlation coefficient in a controllable and tunable way, while keeping both the trait of a power-law degree distribution and the main properties of network's resilience and robustness under failures or attacks. The essence of these observations can be attributed to the fact the deletion of large-degree nodes affects the delicate balance of positive and negative contributions to degree correlation in growing scale-free networks, eventually leading to the emergence of disassortativity. Moreover, these theoretical prediction will get further validation in the empirical networks. We support our claims via numerical results and mathematical analysis, and we propose a generative model for disassortative growing scale-free networks.

Show MeSH
The generative model for disassortative scale-free networks.The vertical axis reports the degree correlation coefficient r, and the horizontal axis reports the degree threshold kth above which nodes are removed with probability p = 0.1 during the upgrowth process of networks. The inset reports the degree distributions for different threshold values. All results are obtained on networks with N = 104 and 〈k〉 = 4.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4269889&req=5

f6: The generative model for disassortative scale-free networks.The vertical axis reports the degree correlation coefficient r, and the horizontal axis reports the degree threshold kth above which nodes are removed with probability p = 0.1 during the upgrowth process of networks. The inset reports the degree distributions for different threshold values. All results are obtained on networks with N = 104 and 〈k〉 = 4.

Mentions: The latter can be realized in the following way. When a new link is formed during the preferential attachment growth, a random node of the existing network with degree larger than a given threshold kth is removed with a fixed probability p (in the following we assume p = 0.1). Fig. 6 reports how the correlation coefficient r for the resulting network depends on kth. Notice that the pruning process here gradually reduces the correlation coefficient and results in the generation of a disassortative mixing pattern associated with a scale-free degree distribution, as shown in the inset of Fig. 6.


Emergence of disassortative mixing from pruning nodes in growing scale-free networks.

Wang SJ, Wang Z, Jin T, Boccaletti S - Sci Rep (2014)

The generative model for disassortative scale-free networks.The vertical axis reports the degree correlation coefficient r, and the horizontal axis reports the degree threshold kth above which nodes are removed with probability p = 0.1 during the upgrowth process of networks. The inset reports the degree distributions for different threshold values. All results are obtained on networks with N = 104 and 〈k〉 = 4.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4269889&req=5

f6: The generative model for disassortative scale-free networks.The vertical axis reports the degree correlation coefficient r, and the horizontal axis reports the degree threshold kth above which nodes are removed with probability p = 0.1 during the upgrowth process of networks. The inset reports the degree distributions for different threshold values. All results are obtained on networks with N = 104 and 〈k〉 = 4.
Mentions: The latter can be realized in the following way. When a new link is formed during the preferential attachment growth, a random node of the existing network with degree larger than a given threshold kth is removed with a fixed probability p (in the following we assume p = 0.1). Fig. 6 reports how the correlation coefficient r for the resulting network depends on kth. Notice that the pruning process here gradually reduces the correlation coefficient and results in the generation of a disassortative mixing pattern associated with a scale-free degree distribution, as shown in the inset of Fig. 6.

Bottom Line: Disassortative mixing is ubiquitously found in technological and biological networks, while the corresponding interpretation of its origin remains almost virgin.We here give evidence that pruning the largest-degree nodes of a growing scale-free network has the effect of decreasing the degree correlation coefficient in a controllable and tunable way, while keeping both the trait of a power-law degree distribution and the main properties of network's resilience and robustness under failures or attacks.We support our claims via numerical results and mathematical analysis, and we propose a generative model for disassortative growing scale-free networks.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics, Shaanxi Normal University, Xi'An City, ShaanXi Province, China.

ABSTRACT
Disassortative mixing is ubiquitously found in technological and biological networks, while the corresponding interpretation of its origin remains almost virgin. We here give evidence that pruning the largest-degree nodes of a growing scale-free network has the effect of decreasing the degree correlation coefficient in a controllable and tunable way, while keeping both the trait of a power-law degree distribution and the main properties of network's resilience and robustness under failures or attacks. The essence of these observations can be attributed to the fact the deletion of large-degree nodes affects the delicate balance of positive and negative contributions to degree correlation in growing scale-free networks, eventually leading to the emergence of disassortativity. Moreover, these theoretical prediction will get further validation in the empirical networks. We support our claims via numerical results and mathematical analysis, and we propose a generative model for disassortative growing scale-free networks.

Show MeSH