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Random scale-free networks are ultrasmall worlds. The average length of the shortest paths in networks of size N scales as lnlnN. Here we show that these ultrasmall worlds can be navigated in ultrashort time. Greedy routing on scale-free…
The availability of data from many different sources and fields of science has made it possible to map out an increasing number of networks of contacts and interactions. However, quantifying how reliable these data are remains an open…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
Statistical properties of position-dependent ball-passing networks in real football games are examined. We find that the networks have the small-world property, and their degree distributions are fitted well by a truncated gamma…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
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.…
We consider information diffusion on Web-like networks and how random walks can simulate it. A well-studied problem in this domain is Partial Cover Time, i.e., the calculation of the expected number of steps a random walker needs to visit a…
Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on…
Networks with a given degree distribution may be very resilient to one type of failure or attack but not to another. The goal of this work is to determine network design guidelines which maximize the robustness of networks to both random…
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…
In recent work, Jon Kleinberg considered a small-world network model consisting of a d-dimensional lattice augmented with shortcuts. The probability of a shortcut being present between two points decays as a power of the distance between…
Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be…
Random walks on discrete lattices are fundamental models that form the basis for our understanding of transport and diffusion processes. For a single random walker on complex networks, many properties such as the mean first passage time and…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…
This paper mainly investigates why small-world networks are navigable and how to navigate small-world networks. We find that the navigability can naturally emerge from self-organization in the absence of prior knowledge about underlying…
We consider global optimization problems, where the feasible region $\X$ is a compact subset of $\mathbb{R}^d$ with $d \geq 10$. For these problems, we demonstrate the following. First: the actual convergence of global random search…
We investigate diffusive search on planar networks, motivated by tubular organelle networks in cell biology that contain molecules searching for reaction partners and binding sites. Exact calculation of the diffusive mean first-passage time…
This research addresses the challenge of performing search missions in dynamic environments, particularly for drifting targets whose movement is dictated by a flow field. This is accomplished through a dynamical system that integrates two…