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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.

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(a) Size of the giant connected component S (normalized to the network size), mean size of isolated clusters 〈s〉, and (b) clustering coefficient C, as functions of the fraction of removed nodes f. Here, it is worth mentioning that we focus on the case of pruning the largest-degree nodes in (a), yet provide a brief comparison of three strategies in (b). Same stipulations as in the Caption of Fig. 1.
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f3: (a) Size of the giant connected component S (normalized to the network size), mean size of isolated clusters 〈s〉, and (b) clustering coefficient C, as functions of the fraction of removed nodes f. Here, it is worth mentioning that we focus on the case of pruning the largest-degree nodes in (a), yet provide a brief comparison of three strategies in (b). Same stipulations as in the Caption of Fig. 1.

Mentions: Furthermore, SF networks are usually vulnerable to attacks targeting the largest-degree nodes29. It is then instructive to monitor the impact of pruning such nodes on the giant connected component of the network. Figure 3(a) reports the size of the giant cluster S, normalized by the network size, and the mean size of other isolated clusters 〈s〉, versus the fraction of removed nodes f. With the increment of f, the giant cluster size S suffers just a very slight decline, while the mean size of isolated clusters remains close to 1.0. Besides, another typical property of complex networks is the clustering coefficient C930, which is used to measure the whole connection of networks. Figure 3(b) shows the variance of clustering coefficient C in dependence on the fraction of removed nodes f for three strategies. It is clear that pruning the largest-degree nodes obviously decreases the cluster coefficient C, which means that the fraction of connected triples of nodes decline. These results thus indicate that the disassortative SF networks, resulting from the deletion of largest-degree nodes, still consist of a unique giant cluster with size , yet slightly low clustering coefficient.


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

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

(a) Size of the giant connected component S (normalized to the network size), mean size of isolated clusters 〈s〉, and (b) clustering coefficient C, as functions of the fraction of removed nodes f. Here, it is worth mentioning that we focus on the case of pruning the largest-degree nodes in (a), yet provide a brief comparison of three strategies in (b). Same stipulations as in the Caption of Fig. 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: (a) Size of the giant connected component S (normalized to the network size), mean size of isolated clusters 〈s〉, and (b) clustering coefficient C, as functions of the fraction of removed nodes f. Here, it is worth mentioning that we focus on the case of pruning the largest-degree nodes in (a), yet provide a brief comparison of three strategies in (b). Same stipulations as in the Caption of Fig. 1.
Mentions: Furthermore, SF networks are usually vulnerable to attacks targeting the largest-degree nodes29. It is then instructive to monitor the impact of pruning such nodes on the giant connected component of the network. Figure 3(a) reports the size of the giant cluster S, normalized by the network size, and the mean size of other isolated clusters 〈s〉, versus the fraction of removed nodes f. With the increment of f, the giant cluster size S suffers just a very slight decline, while the mean size of isolated clusters remains close to 1.0. Besides, another typical property of complex networks is the clustering coefficient C930, which is used to measure the whole connection of networks. Figure 3(b) shows the variance of clustering coefficient C in dependence on the fraction of removed nodes f for three strategies. It is clear that pruning the largest-degree nodes obviously decreases the cluster coefficient C, which means that the fraction of connected triples of nodes decline. These results thus indicate that the disassortative SF networks, resulting from the deletion of largest-degree nodes, still consist of a unique giant cluster with size , yet slightly low clustering coefficient.

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