Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that these two features are the consequence of a hierarchical organization, implying that small groups of nodes organize in a hierarchical manner into increasingly large groups, while maintaining a scale-free topology. In hierarchical networks, the deg...

Many real networks in nature and society share two generic properties: they are scale-free and they display a high degree of clustering. We show that the scalefree nature and high clustering of real networks are the consequence of a hierarchical organization, implying that small groups of nodes form increasingly large groups in a hierarchical manner, while maintaining a scale-free topology. In ...

It has recently been shown that many networks associated with complex systems are small-world (they have both a large local clustering and a small average distance and diameter) and they are also scale-free (the degrees are distributed according to a power-law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems which are modeled. While most of ...

We present a procedural method for generating hierarchical road networks connecting cities, towns and villages over large terrains. Our approach relies on an original geometric graph generation algorithm based on a nonEuclidean metric combined with a path merging algorithm that creates junctions between the different types of roads. Unlike previous work, our method allows high level user contro...

Memory networks are neural networks with an explicit memory component that can be both read and written to by the network. The memory is often addressed in a soft way using a softmax function, making end-to-end training with backpropagation possible. However, this is not computationally scalable for applications which require the network to read from extremely large memories. On the other hand,...

This paper proposes an analytical framework for peer-to-peer (P2P) networks and introduces schemes for building P2P networks to approach the minimum weighted average download time (WADT). In the considered P2P framework, the server, which has the information of all the download bandwidths and upload bandwidths of the peers, minimizes the weighted average download time by determining the optimal...

Many real world networks are reported to have hierarchically modular organization. However, there exists no algorithm-independent metric to characterize hierarchical modularity in a complex system. The main results of the paper are a set of methods to address this problem. First, classical results from random matrix theory are used to derive the spectrum of a typical stochastic block model hier...

The huge increase of wireless networks imposed the need of managing very large networks in an efficient way. A usual structure that is utilized towards this goal is the hierarchical structure. We consider the Frequency Assignment Problems in very large networks can be constructed by a set of much smaller netwroks connected to each other in a hierarchical, tree-like way. We focus on planar case,...

In this work we introduce two practical and interesting models of ad-hoc mobile networks: a) hierarchical ad-hoc networks, comprised of dense subnetworks of mobile users interconnected by a very fast yet limited backbone infrastructure, b) highly changing ad-hoc networks, where the deployment area changes in a highly dynamic way and is unknown to the protocol. In such networks, we study the pro...

The idea that complex systems have a hierarchical modular organization originated in the early 1960s and has recently attracted fresh support from quantitative studies of large scale, real-life networks. Here we investigate the hierarchical modular (or "modules-within-modules") decomposition of human brain functional networks, measured using functional magnetic resonance imaging in 18 healthy v...