Spatially embedded random networks

Many real-world networks analyzed in modern network theory have a natural spatial element; e.g., the Internet, social networks, neural networks, etc. Yet, aside from a comparatively small number of somewhat specialized and domain-specific studies, the spatial element is mostly ignored and, in particular, its relation to network structure disregarded. In this paper we introduce a model framework to analyze the mediation of network structure by spatial embedding; specifically, we model connectivity as dependent on the distance between network nodes. Our spatially embedded random networks construction is not primarily intended as an accurate model of any specific class of real-world networks, but rather to gain intuition for the effects of spatial embedding on network structure; nevertheless we are able to demonstrate, in a quite general setting, some constraints of spatial embedding on connectivity such as the effects of spatial symmetry, conditions for scale free degree distributions and the existence of small-world spatial networks. We also derive some standard structural statistics for spatially embedded networks and illustrate the application of our model framework with concrete examples

Spatial networks with wireless applications

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex,non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina

Temporal Networks

A great variety of systems in nature, society and technology -- from the web of sexual contacts to the Internet, from the nervous system to power grids -- can be modeled as graphs of vertices coupled by edges. The network structure, describing how the graph is wired, helps us understand, predict and optimize the behavior of dynamical systems. In many cases, however, the edges are not continuously active. As an example, in networks of communication via email, text messages, or phone calls, edges represent sequences of instantaneous or practically instantaneous contacts. In some cases, edges are active for non-negligible periods of time: e.g., the proximity patterns of inpatients at hospitals can be represented by a graph where an edge between two individuals is on throughout the time they are at the same ward. Like network topology, the temporal structure of edge activations can affect dynamics of systems interacting through the network, from disease contagion on the network of patients to information diffusion over an e-mail network. In this review, we present the emergent field of temporal networks, and discuss methods for analyzing topological and temporal structure and models for elucidating their relation to the behavior of dynamical systems. In the light of traditional network theory, one can see this framework as moving the information of when things happen from the dynamical system on the network, to the network itself. Since fundamental properties, such as the transitivity of edges, do not necessarily hold in temporal networks, many of these methods need to be quite different from those for static networks

Socioeconomic Networks with Long-Range Interactions

We study a modified version of a model previously proposed by Jackson and Wolinsky to account for communicating information and allocating goods in socioeconomic networks. In the model, the utility function of each node is given by a weighted sum of contributions from all accessible nodes. The weights, parameterized by the variable $\delta$, decrease with distance. We introduce a growth mechanism where new nodes attach to the existing network preferentially by utility. By increasing $\delta$, the network structure evolves from a power-law to an exponential degree distribution, passing through a regime characterised by shorter average path length, lower degree assortativity and higher central point dominance. In the second part of the paper we compare different network structures in terms of the average utility received by each node. We show that power-law networks provide higher average utility than Poisson random networks. This provides a possible justification for the ubiquitousness of scale-free networks in the real world.Comment: 11 pages, 8 figures, minor correction

Research on Wireless Multi-hop Networks: Current State and Challenges

Wireless multi-hop networks, in various forms and under various names, are being increasingly used in military and civilian applications. Studying connectivity and capacity of these networks is an important problem. The scaling behavior of connectivity and capacity when the network becomes sufficiently large is of particular interest. In this position paper, we briefly overview recent development and discuss research challenges and opportunities in the area, with a focus on the network connectivity.Comment: invited position paper to International Conference on Computing, Networking and Communications, Hawaii, USA, 201

Image informatics strategies for deciphering neuronal network connectivity

Brain function relies on an intricate network of highly dynamic neuronal connections that rewires dramatically under the impulse of various external cues and pathological conditions. Among the neuronal structures that show morphologi- cal plasticity are neurites, synapses, dendritic spines and even nuclei. This structural remodelling is directly connected with functional changes such as intercellular com- munication and the associated calcium-bursting behaviour. In vitro cultured neu- ronal networks are valuable models for studying these morpho-functional changes. Owing to the automation and standardisation of both image acquisition and image analysis, it has become possible to extract statistically relevant readout from such networks. Here, we focus on the current state-of-the-art in image informatics that enables quantitative microscopic interrogation of neuronal networks. We describe the major correlates of neuronal connectivity and present workflows for analysing them. Finally, we provide an outlook on the challenges that remain to be addressed, and discuss how imaging algorithms can be extended beyond in vitro imaging studies