Related papers: Scale free networks from a Hamiltonian dynamics
We evolve network topology of an asymmetrically connected threshold network by a simple local rewiring rule: quiet nodes grow links, active nodes lose links. This leads to convergence of the average connectivity of the network towards the…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
We generalize the degree-organizational view of real-world networks with broad degree-distributions in a landscape analogue with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent…
A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$…
Many real-world networks have properties of small-world networks, with clustered local neighborhoods and low average-shortest path (ASP). They may also show a scale-free degree distribution, which can be generated by growth and preferential…
Synchronization problems in complex networks are very often studied by researchers due to its many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, Scale Free networks with degree…
In heterogeneous network systems such as ecological and social networks, structural stability depends on how connectivity changes under node removal, as different removal sequences can trigger distinct modes of systemic collapse. While…
In this work we extend the model of Bonabeau et al. in the case of scale-free networks. A sharp transition is observed from an egalitarian to an hierarchical society, with a very low population density threshold. The exact threshold value…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
The statistical property of a growing scale-free network is studied based on an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett. 86, 5401 (2001)], with the additional constraints of forbidden of self-connection and…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
All crucial features of the recently observed real-world weighted networks are obtained in a model where the weight of a link is defined with a single non-linear parameter $\alpha$ as $w_{ij}=(s_is_j)^\alpha$, $s_i$ and $s_j$ are the…
A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
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 explicated. We investigate the dynamic behaviors of resource/traffic flow on scale-free…
We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…
We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…
In the past few years, the discoveries of small-world and scale-free properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the…
The Watts-Strogatz algorithm transferring a regular lattice to the small world network is modified by introducing preferential rewiring constrained by connectivity demand. The probability to link to/ unlink form a node is dependent on a…
We extend the standard scale-free network model to include a ``triad formation step''. We analyze the geometric properties of networks generated by this algorithm both analytically and by numerical calculations, and find that our model…
There is increasing evidence that dense networks occur in on-line social networks, recommendation networks and in the brain. In addition to being dense, these networks are often also scale-free, i.e. their degree distributions follow…