Related papers: Harmony in the Small-World
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 study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance,…
Great part of the interest in complex networks has been motivated by the presence of structured, frequently non-uniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they…
A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the…
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…
Frigyes Karinthy, in his 1929 short story "L\'aancszemek" ("Chains") suggested that any two persons are distanced by at most six friendship links. (The exact wording of the story is slightly ambiguous: "He bet us that, using no more than…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
Many real-world networks are large, complex and thus hard to understand, analyze or visualize. The data about networks is not always complete, their structure may be hidden or they change quickly over time. Therefore, understanding how…
We draw attention to a clear dichotomy between small-world networks exhibiting exponential neighborhood growth, and fractal-like networks where neighborhoods grow according to a power law. This distinction is observed in a number of…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
During the last three decades the Internet has experienced fascinating evolution, both exponential growth in traffic and rapid expansion in topology. The size of the Internet becomes enormous, yet the network is very `small' in the sense…
We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a…
Many real-world complex systems such as social, biological, information as well as technological systems results of a decentralized and unplanned evolution which leads to a common structuration. Irrespective of their origin, these so-called…
We proposed a deterministic multidimensional growth model for small-world networks. The model can characterize the distinguishing properties of many real-life networks with geometric space structure. Our results show the model possesses…
Despite the growing interest in characterizing the local geometry leading to the global topology of networks, our understanding of the local structure of complex networks, especially real-world networks, is still incomplete. Here, we…
The concept of small worlds is introduced into the physical topology of wireless networks in this work. A. Helmy provided two con- struction schemes of small worlds for the wireless networks, link rewiring and link addition, but he mainly…
A class of cubic networks composed of a regular one-dimensional lattice and a set of long-range links is introduced. Networks parametrized by a positive integer k are constructed by starting from a one-dimensional lattice and iteratively…
Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show…
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…