Network motifs are overrepresented interconnection patterns found in real-world networks. What functional advantages may they offer for building complex systems? We show that most network motifs emerge from interconnections patterns that best exploit the intrinsic stability characteristics of individual nodes. This feature is observed at different scales in a network, from nodes to modules, suggesting an efficient mechanism to stably build complex systems.
A classic measure of ecological stability describes the tendency of a community to return to equilibrium after small perturbation. While many advances show how the network structure of these communities severely constrains such tendencies, few if any of these advances address one of the most fundamental properties of network structure: heterogeneity among nodes with different numbers of links. Here we systematically explore this property of degree heterogeneity and find that its effects on stability systematically vary with different types of interspecific interactions. Degree heterogeneity is always destabilizing in ecological networks with both competitive and mutualistic interactions while its effects on networks of predator-prey interactions such as food webs depend on prey contiguity, i.e., the extent to which the species consume an unbroken sequence of prey in community niche space. Increasing degree heterogeneity stabilizes food webs except those with the most contiguity. These findings help explain previously unexplained observations that food webs are highly but not completely contiguous and, more broadly, deepens our understanding of the stability of complex ecological networks with important implications for other types of dynamical systems.
Controlling complex networked systems to a desired state is a key research goal in contemporary science. Despite recent advances in studying the impact of network topology on controllability, a comprehensive understanding of the synergistic effect of network topology and individual dynamics on controllability is still lacking. Here we offer a theoretical study with particular interest in the diversity of dynamic units characterized by different types of individual dynamics. Interestingly, we find a global symmetry accounting for the invariance of controllability with respect to exchanging the densities of any two different types of dynamic units, irrespective of the network topology. The highest controllability arises at the global symmetry point, at which different types of dynamic units are of the same density. The lowest controllability occurs when all self-loops are either completely absent or present with identical weights. These findings further improve our understanding of network controllability and have implications for devising the optimal control of complex networked systems in a wide range of fields.
Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. According to prospect theory, people are risk-averse with respect to gains and risk-seeking with respect to losses, a phenomenon called loss aversion. Despite of the fact that prospect theory has been well developed in behavioral economics at the theoretical level, there exist very few large-scale empirical studies and most of them have been undertaken with micro-panel data. Here we analyze over 28.5 million trades made by 81.3 thousand traders of an online financial trading community over 28 months, aiming to explore the large-scale empirical aspect of prospect theory. By analyzing and comparing the behavior of winning and losing trades and traders, we find clear evidence of the loss aversion phenomenon, an essence in prospect theory. This work hence demonstrates an unprecedented large-scale empirical evidence of prospect theory, which has immediate implication in financial trading, e.g., developing new trading strategies by minimizing the effect of loss aversion. Moreover, we introduce three risk-adjusted metrics inspired by prospect theory to differentiate winning and losing traders based on their historical trading behavior. This offers us potential opportunities to augment online social trading, where traders are allowed to watch and follow the trading activities of others, by predicting potential winners statistically based on their historical trading behavior rather than their trading performance at any given point in time.
We study the Japan and U.S. patent records of several decades to demonstrate the effect of collaboration on innovation. We find that statistically inventor teams slightly outperform solo inventors while company teams perform equally well as solo companies. By tracking the performance record of individual teams we find that inventor teams performance generally degrades with more repeat collaborations. Though company teams performance displays strongly bursty behavior, long-term collaboration does not significantly help innovation at all. To systematically study the effect of repeat collaboration, we define the repeat collaboration number of a team as the average number of collaborations over all the teammate pairs. We find that mild repeat collaboration improves the performance of Japanese inventor teams and U.S. company teams. Yet, excessive repeat collaboration does not significantly help innovation at both the inventor and company levels in both countries. To control for unobserved heterogeneity, we perform a detailed regression analysis and the results are consistent with our simple observations. The presented results reveal the intricate effect of collaboration on innovation, which may also be observed in other creative projects.
As a fundamental structural transition in complex networks, core percolation is related to a wide range of important problems. Yet, previous theoretical studies of core percolation have been focusing on the classical ErdH{o}s-Renyi random networks with Poisson degree distribution, which are quite unlike many real-world networks with scale-free or fat-tailed degree distributions. Here we show that core percolation can be analytically studied for complex networks with arbitrary degree distributions. We derive the condition for core percolation and find that purely scale-free networks have no core for any degree exponents. We show that for undirected networks if core percolation occurs then it is always continuous while for directed networks it becomes discontinuous when the in- and out-degree distributions are different. We also apply our theory to real-world directed networks and find, surprisingly, that they often have much larger core sizes as compared to random models. These findings would help us better understand the interesting interplay between the structural and dynamical properties of complex networks.
We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the networks degree distribution. We rigorously prove that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.
