Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

Visibility graphs for fMRI data: multiplex temporal graphs and their modulations across resting state networks

Abstract: Visibility algorithms are a family of methods that map time series into graphs, such that the tools of graph theory and network science can be used for the characterization of time series. This approach has proved a convenient tool and visibility graphs have found applications across several disciplines. Recently, an approach has been proposed to extend this framework to multivariate time series, allowing a novel way to describe collective dynamics. Here we test their application to fMRI time series, following two main motivations, namely that (i) this approach allows to simultaneously capture and process relevant aspects of both local and global dynamics in an easy and intuitive way, and (ii) this provides a suggestive bridge between time series and network theory which nicely fits the consolidating field of network neuroscience. Our application to a large open dataset reveals differences in the similarities of temporal networks (and thus in correlated dynamics) across resting state networks, and gives indications that some differences in brain activity connected to psychiatric disorders could be picked up by this approach.

Dynamic measures for transportation networks.

Abstract: Most complex network analyses of transportation systems use simplified static representations obtained from existing connections in a time horizon. In static representations, travel times, waiting times and compatibility of schedules are neglected, thus losing relevant information. To obtain a more accurate description of transportation networks, we use a dynamic representation that considers synced paths and that includes waiting times to compute shortest paths. We use the shortest paths to define dynamic network, node and edge measures to analyse the topology of transportation networks, comparable with measures obtained from static representations. We illustrate the application of these measures with a toy model and a real transportation network built from schedules of a low-cost carrier. Results show remarkable differences between measures of static and dynamic representations, demonstrating the limitations of the static representation to obtain accurate information of transportation networks.

Social networks and geography: a review of the literature and its implications

Abstract: The spatial metaphor of the network along with its accompanying abstractions, such as flow, movement, and connectivity, have been central themes throughout the relational turn in human geography. However, to date networks in geography have been primarily explored either through actor-network theory or assemblage thinking, both of which embrace the network metaphor without specifically and formally interrogating networks themselves. We seek to problematize the treatment of networks in geography by exploring the largely underutilized literature on social networks as an alternative to the now dominant actor-network and assemblage frameworks. Our paper discusses the conceptual connections between key concepts in geography, such as place, distance, scale, and power, and those in network theory, such as centrality, density, and homophily. Voluntarily written from the periphery of human geography, our paper opens new directions for geographers that are interested in more than the metaphor of the network.

Conceptualising dyadic inter-organisational relationships as complex adaptive systems

Abstract: There is a long tradition of research that recognises that business relations occur within complex systems. Network theory recognises the embedded nature of actor relations; it acknowledges their dynamic and emergent qualities, and foregrounds the co-existence of continuity and change over time (Thorelli 1986; Hakansson and Snehota 1990; Easton 1992; Dubois et al. 2003). Research within this tradition has been underway for nearly two decades and has been largely responsible for the shift in focus from dyadic exchange to exchange between organisational actors within networks (Hakansson and Snehota 1990; Cheung and Turnbull 1998). Despite the recognition here and elsewhere that complexity has much to offer in understanding interaction, relationships and networks, the majority of work to date has focused primarily upon the network. While this is, of course, very interesting, it ignores the possibilities of understanding the dyad as a complex adaptive system in its own right. This paper will show however, that research at the level of the dyad has suffered as a result of the popularity of network theory and also because of the axiomatic reliance on deterministic theories and framework. We suggest that despite the recognition of complexity at the level of the network, the dyad continues to be treated as a fairly simple system and emerging insights from the network approach have not generally been incorporated. While this may be implicitly acknowledged within network research, it has rarely been explored in any detail. To redress this issue, this paper elucidates the possibilities of using complexity theory, a theoretical frame being brought to bear on understanding business networks is complexity theory (Easton et al. 1997; Wilkinson and Young 2003) to the understanding and explaining of patterns of interaction and change within dyads. Moreover, critical realism, already acknowledged as being particularly apposite in network studies (Easton 2000), is brought to bear to aid in the explanation of dyadic relationship development. This position foregrounds the search for the structural conditions and generative mechanisms to explain the nature of the relationship and its development over time. The mobilisation of this position is facilitated by a processual case study design, the nature of which will be outlined in detail.

Graph-time signal processing : Filtering and sampling strategies

Abstract: The necessity to process signals living in non-Euclidean domains, such as signals defined on the top of a graph, has led to the extension of signal processing techniques to the graph setting. Among different approaches, graph signal processing distinguishes itself by providing a Fourier analysis of these signals. Analogously to the Fourier transform for time and image signals, the graph Fourier transform decomposes the graph signals decomposes in terms of the harmonics provided by the underlying topology. For instance, a graph signal characterized by a slow variation between adjacent nodes has a low frequency content. Along with the graph Fourier transform, graph filters are the key tool to alter the graph frequency content of a graph signal. This thesis focuses on graph filters that are performed distributively in the node domain–that is, each node needs to exchange information only within its neighbor to perform a given filtering operation. Similarly to the classical filters, we propose ways to design and implement distributed finite impulse response and infinite impulse response graph filters. One of the key contributions of this thesis is to bring the temporal dimension to graph signal processing and build upon a graph-time signal processing framework. This is done in different ways. First, we analyze the effects that the temporal variations on the graph signal and graph topology have on the filtering output. Second, we introduce the notion of joint graph-time filtering. Third, we presentpr a statistical analysis of the distributed graph filtering when the graph signal and the graph topology change randomly in time. Finally, we extend the sampling framework from the reconstruction of graph signals to the observation and tracking of time-varying graph processes. We characterize the behavior of the distributed autoregressivemoving average (ARMA) graph filters when the graph signal and the graph topology are time-varying. The latter analysis is exploited in two ways: i ) to quantify the limitations of graph filters in a dynamic environment, such as a moving sensors processing a time-varying signal in a sensor network; and i i ) to provide ways for filtering with low computation and communication complexity time-varying graph signals. We develop the notion of distributed graph-time filtering, which is an operation that jointly processes the graph frequencies of a time-varying graph signal on one hand and its temporal frequencies on the other hand. We propose distributed finite impulse response and infinite impulse response recursions to implement a two-dimensional graphtime filtering operation. Finally, we propose design strategies to find the filter coefficients that approximate a desired two-dimensional frequency response. We extend the analysis of graph filters to a stochastic environment, i.e., when the graph topology and the graph signal change randomly over time. By characterizing the first and second order moments of the filter output, we quantify the impact of the graph signal and the graph topology randomness into the distributed filtering operation. The latter allows us to develop the notion of graph filtering in the mean, which is also used to ease the computational burden of classical graph filters. Finally, we propose a sampling framework for time-varying graph signals. Particularly, when the graph signal changes over time following a state-space model, we extend the graph signal sampling theory to the tasks of observing and tracking the time-varying graph signal froma few relevant nodes. The latter theory considers the graph signal sampling as a particular case and shows that tools from sparse sensing and sensor selection can be used for sampling.