Mutual selection model for weighted networks

The geometric nature of weights in real complex networks

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.

Complex networks have been conjectured to be hidden in metric spaces, which offer geometric interpretation of networks' topologies. Here the authors extend this concept to weighted networks, providing empirical evidence on the metric natures of weights, which are shown to be reproducible by a gravity model.

Geometric origin of scaling in large traffic networks

Large scale traffic networks are an indispensable part of contemporary human mobility and international trade. Networks of airport travel and cargo ship movements are invaluable for the understanding of human mobility patterns [R. Guimera et al., Proc. Natl. Acad. Sci. U.S.A. 102, 7794 (2005))], epidemic spreading [V. Colizza et al., Proc. Natl. Acad. Sci. U.S.A. 103, 2015 (2006)], global trade [International Maritime Organization, http://www.imo.org/], and spread of invasive species [G. M. Ruiz et al., Nature (London) 408, 49 (2000)]. Different studies [M. Barthelemy, Phys. Rept. 499, 1 (2011)] point to the universal character of some of the exponents measured in such networks. Here we show that exponents which relate (i) the strength of nodes to their degree and (ii) weights of links to degrees of nodes that they connect have a geometric origin. We present a simple robust model which exhibits the observed power laws and relates exponents to the dimensionality of 2D space in which traffic networks are embedded. We show that the relation between weight strength and degree is s(k)~k(3/2), the relation between distance strength and degree is s(d)(k)~k(3/2), and the relation between weight of link and degrees of linked nodes is w(ij)~(k(i)k(j))(1/2) on the plane 2D surface. We further analyze the influence of spherical geometry, relevant for the whole planet, on exact values of these exponents. Our model predicts that these exponents should be found in future studies of port networks and it imposes constraints on more refined models of port networks.

Power-law strength-degree correlation from resource-allocation dynamics on weighted networks

Many weighted scale-free networks are known to have a power-law correlation between strength and degree of nodes, which, however, has not been well explained. We investigate the dynamic behavior of resource-traffic flow on scale-free networks. The dynamical system will evolve into a kinetic equilibrium state, where the strength, defined by the amount of resource or traffic load, is correlated with the degree in a power-law form with tunable exponent. The analytical results agree well with simulations.

Modeling the coevolution of topology and traffic on weighted technological networks

For many technological networks, the network structures and the traffic taking place on them mutually interact. The demands of traffic increment spur the evolution and growth of the networks to maintain their normal and efficient functioning. In parallel, a change of the network structure leads to redistribution of the traffic. In this paper, we perform an extensive numerical and analytical study, extending results of Wang [Phys. Rev. Lett. 94, 188702 (2005)]. By introducing a general strength-coupling interaction driven by the traffic increment between any pair of vertices, our model generates networks of scale-free distributions of strength, weight, and degree. In particular, the obtained nonlinear correlation between vertex strength and degree, and the disassortative property demonstrate that the model is capable of characterizing weighted technological networks. Moreover, the generated graphs possess both dense clustering structures and an anticorrelation between vertex clustering and degree, which are widely observed in real-world networks. The corresponding theoretical predictions are well consistent with simulation results.

Evolving Apollonian networks with small-world scale-free topologies

We propose two types of evolving networks: evolutionary Apollonian networks (EANs) and general deterministic Apollonian networks (GDANs), established by simple iteration algorithms. We investigate the two networks by both simulation and theoretical prediction. Analytical results show that both networks follow power-law degree distributions, with distribution exponents continuously tuned from 2 to 3. The accurate expression of clustering coefficient is also given for both networks. Moreover, the investigation of the average path length of EAN and the diameter of GDAN reveals that these two types of networks possess small-world feature. In addition, we study the collective synchronization behavior on some limitations of the EAN.

Efficient routing on complex networks

We propose a routing strategy to improve the transportation efficiency on complex networks. Instead of using the routing strategy for shortest path, we give a generalized routing algorithm to find the so-called efficient path, which considers the possible congestion in the nodes along actual paths. Since the nodes with the largest degree are very susceptible to traffic congestion, an effective way to improve traffic and control congestion, as our strategy, can be redistributing traffic load in central nodes to other noncentral nodes. Simulation results indicate that the network capability in processing traffic is improved more than 10 times by optimizing the efficient path, which is in good agreement with the analysis.

Mutual attraction model for both assortative and disassortative weighted networks

For most complex networks, the connection between a pair of nodes is the result of their mutual affinity and attachment. In this letter, we will propose a mutual attraction model to characterize weighted evolving networks. By introducing the initial attractiveness A and the general mechanism of mutual attraction (controlled by parameter m), our model can naturally reproduce scale-free distributions of degree, weight, and strength, as found in many real systems. Also, simulation results are consistent with theoretical predictions. Interestingly, we obtain nontrivial clustering coefficient C and tunable degree assortativity r, depending on the values of m and A. Our model appears as a more general one that unifies the characterization of both assortative and disassortative weighted networks.