相关论文: True scale-free networks hidden by finite size eff…

We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…

We show that the error of iteratively magnitude-pruned networks empirically follows a scaling law with interpretable coefficients that depend on the architecture and task. We functionally approximate the error of the pruned networks,…

We analyse the statistical properties of public transport networks. These networks are defined by a set of public transport routes (bus lines) and the stations serviced by these. For larger networks these appear to possess a scale-free…

We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We…

Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free…

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…

This article addresses the degree distribution of subnetworks, namely the number of links between the nodes in each subnetwork and the remainder of the structure (cond-mat/0408076). The transformation from a subnetwork-partitioned model to…

It has been claimed that protein-protein interaction (PPI) networks are scale-free based on the observation that the node degree sequence follows a power law. Here we argue that these claims are likely to be based on erroneous statistical…

Real world networks have, for a long time, been modelled by scale-free networks, which have many sparsely connected nodes and a few highly connected ones (the hubs). However, both in society and in biology, a new structure must be…

The concept of network efficiency, recently proposed to characterize the properties of small-world networks, is here used to study the effects of errors and attacks on scale-free networks. Two different kinds of scale-free networks, i.e.…

We model power grids as graphs with heavy-tailed sinks, which represent demand from cities, and study cascading failures on such graphs. Our analysis links the scale-free nature of blackout sizes to the scale-free nature of city sizes,…

Recently, Broido & Clauset (2019) mentioned that (strict) Scale-Free networks were rare, in real life. This might be related to the statement of Stumpf, Wiuf & May (2005), that sub-networks of scale-free networks are not scale-free. In the…

Small-world architectures may be implicated in a range of phenomena from disease propagation to networks of neurons in the cerebral cortex. While most of the recent attention on small-world networks has focussed on the effect of introducing…

It is generally accepted that scale-free networks is prone to epidemic spreading allowing the onset of large epidemics whatever the spreading rate of the infection. In the paper, we show that disease propagation may be suppressed in…

Modeling human dynamics responsible for the formation and evolution of the so-called social networks - structures comprised of individuals or organizations and indicating connectivities existing in a community - is a topic recently…

In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…

We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…

Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…

Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)\approx…