Related papers: Statistical Complexity of Heterogeneous Geometric …
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
The ability to share social network data at the level of individual connections is beneficial to science: not only for reproducing results, but also for researchers who may wish to use it for purposes not foreseen by the data releaser.…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabasi-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing…
A key measure that has been used extensively in analyzing complex networks is the degree of a node (the number of the node's neighbors). Because of its discrete nature, when the degree measure was used in analyzing weighted networks,…
Methods from statistical physics, such as those involving complex networks, have been increasingly used in quantitative analysis of linguistic phenomena. In this paper, we represented pieces of text with different levels of simplification…
The intricate relations between elements in natural and human-made systems sustain the complex processes that shape our world, forming multiscale networks of interactions. These networks can be represented as graphs composed of nodes…
Many real-world network are multilayer, with nontrivial correlations across layers. Here we show that these correlations amplify geometry in networks. We focus on mutual clustering--a measure of the amount of triangles that are present in…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has…
Higher order networks are able to characterize data as different as functional brain networks, protein interaction networks and social networks beyond the framework of pairwise interactions. Most notably higher order networks include…
A simple and accurate relationship is demonstrated that links the average shortest path, nodes, and edges in a complex network. This relationship takes advantage of the concept of link density and shows a large improvement in fitting…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
Bayesian networks are now being used in enormous fields, for example, diagnosis of a system, data mining, clustering and so on. In spite of their wide range of applications, the statistical properties have not yet been clarified, because…
We introduce the concept of natural connectivity as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It characterizes the redundancy of alternative paths…
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…