Numerous concise models such as preferential attachment have been put forward to reveal the evolution mechanisms of real-world networks, which show that real-world networks are usually jointly driven by a hybrid mechanism of multiplex features instead of a single pure mechanism. To get an accurate simulation for real networks, some researchers proposed a few hybrid models by mixing multiple evolution mechanisms. Nevertheless, how a hybrid mechanism of multiplex features jointly influence the network evolution is not very clear. In this study, we introduce two methods (link prediction and likelihood analysis) to measure multiple evolution mechanisms of complex networks. Through tremendous experiments on artificial networks, which can be controlled to follow multiple mechanisms with different weights, we find the method based on likelihood analysis performs much better and gives very accurate estimations. At last, we apply this method to some real-world networks which are from different domains (including technology networks and social networks) and different countries (e.g., USA and China), to see how popularity and clustering coevolve. We find most of them are affected by both popularity and clustering, but with quite different weights. Many social, technological networks evolve over time after they are established. Previous studies have revealed that real networks possess many different structural features, like various degree distribution 1 , different levels of clustering 2 , existent or nonexistent communities 3 , assortative or disassortative mixing pattern 4 , long or short average shortest distance, and so on, which attract much attention on building models to mimic the network evolution 5, 6 . Meanwhile, the latent mechanisms are also fruitful such as the rich-get-richer 7 , the good-get-richer 8 , the stability constrains 9 , homophily 10 , clustering 11 etc. However, using one pure mechanism is usually insufficient to depict real-world networks precisely because of those different aspects of features. Therefore, researchers mixed different mechanisms in order to get better simulation, like the mixture of clustering and preferential attachment 11, 12 , popularity and randomness 13 , popularity and similarity 14 , topology distance and geographical distance 15 , and so on. In all, networks are likely to be driven by multiple mechanisms, and we are inspired to raise a question: is it possible to measure the contribution of each mechanism in the network evolution? The inchoate way to evaluate network model or underlying mechanism is based on the comparison between some selected structural features. It supposes a model is better than another one if its generated network is more close to the target network in terms of those selected features. But such method cannot be well validated since no one has the fair standard to select representative ones from countless structural features. Without considering any specific structural feature, we had proposed a method based on likelihood analysis to fairly evaluate network models 16 . Therein, we can calculate the appearing likelihood for each newly created link according to the model's mechanism, and then multiply them together to get the likelihood of the set of new links. For a group of models, the one giving the highest likelihood is
Zhang et al. REF introduced the likelihood analysis method to quantify the contribution of different evolutionary mechanisms.
Measuring multiple evolution mechanisms of complex networks
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