Related papers: Multiple Scales in Small-World Graphs
Recently, one paper in Nature(Papadopoulos, 2012) raised an old debate on the origin of the scale-free property of complex networks, which focuses on whether the scale-free property origins from the optimization or not. Because the…
In this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter $q$. Our results…
Hyperbolicity is a property of a graph that may be viewed as being a "soft" version of a tree, and recent empirical and theoretical work has suggested that many graphs arising in Internet and related data applications have hyperbolic…
We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…
Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…
Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place.…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
Complex networks have been studied extensively due to their relevance to many real systems as diverse as the World-Wide-Web (WWW), the Internet, energy landscapes, biological and social networks…
A classic experiment by Milgram shows that individuals can route messages along short paths in social networks, given only simple categorical information about recipients (such as "he is a prominent lawyer in Boston" or "she is a Freshman…
The connectivity of a network contains information about the relationships between nodes, which can denote interactions, associations, or dependencies. We show that this information can be analyzed by measuring the uncertainty (and…
A given neural network in the brain is involved in many different tasks. This implies that, when considering a specific task, the network's connectivity contains a component which is related to the task and another component which can be…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
Networks observed in the real world often have many short loops. This violates the tree-like assumption that underpins the majority of random graph models and most of the methods used for their analysis. In this paper we sketch possible…
Real-world networks exhibit prominent hierarchical and modular structures, with various subgraphs as building blocks. Most existing studies simply consider distinct subgraphs as motifs and use only their numbers to characterize the…
Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…
Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…
In most studies, street networks are considered as undirected graphs while one-way streets and their effect on shortest paths are usually ignored. Here, we first study the empirical effect of one-way streets in about $140$ cities in the…
The presence of hierarchy in many real-world networks is not yet fully explained. Complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for…
We propose a generalization of small world networks, in which the reconnection of links is governed by a function that depends on the distance between the elements to be linked. An adequate choice of this function lets us control the…
Classic measures of graph centrality capture distinct aspects of node importance, from the local (e.g., degree) to the global (e.g., closeness). Here we exploit the connection between diffusion and geometry to introduce a multiscale…