Related papers: On Small-World Networks: Survey and Properties Ana…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation,…
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…
Dating back to two famous experiments by the social-psychologist, Stanley Milgram, in the 1960s, the small-world phenomenon is the idea that all people are connected through a short chain of acquaintances that can be used to route messages.…
We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small…
A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…
Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring…
Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique…
Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…
Networks built to model real world phenomena are characeterised by some properties that have attracted the attention of the scientific community: (i) they are organised according to community structure and (ii) their structure evolves with…
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
Subgraph counts - in particular the number of occurrences of small shapes such as triangles - characterize properties of random networks, and as a result have seen wide use as network summary statistics. However, subgraphs are typically…
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…
Data classification techniques partition the data or feature space into smaller sub-spaces, each corresponding to a specific class. To classify into subspaces, physical features e.g., distance and distributions are utilized. This approach…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
This paper introduces how human languages can be studied in light of recent development of network theories. There are two directions of exploration. One is to study networks existing in the language system. Various lexical networks can be…
One of the most important features observed in real networks is that, as a network's topology evolves so does the network's ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain…
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…
The discovery of small world and scale free properties of many real world networks has revolutionized the way we study, analyze, model and process networks. An important way to analyze these complex networks is to visualize them using graph…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…