From static to temporal network theory – applications to functional brain connectivity

Abstract

Network neuroscience has become an established paradigm to tackle questions related to the functional and structural connectome of the brain. Recently, there has been a growing interest to examine the temporal dynamics of the brain's network activity. While different approaches to capture fluctuations in brain connectivity have been proposed, there have been few attempts to quantify these fluctuations using temporal network theory. Temporal network theory is an extension of network theory that has been successfully applied to the modeling of dynamic processes in economics, social sciences and engineering. The objective of this paper is twofold: (i) to present a detailed description of the central tenets and outline measures from temporal network theory; (ii) apply these measures to a resting-state fMRI dataset to illustrate their utility. Further, we discuss the interpretation of temporal network theory in the context of the dynamic functional brain connectome. All the temporal network measures and plotting functions described in this paper are freely available as a python package Teneto. (7,8,9), yielding knowledge about functional network properties (10,11,12,13) which has been applied to clinical populations (14,15).In parallel to research on the brain's connectome, there has been a focus on studying the dynamics of brain activity. When the brain is modeled as a dynamic system, a diverse range of properties can be explored, prominent examples of this are metastability (16,17,18,19,20) and oscillations (21,22,23). Brain oscillations, inherently dynamic, have become a vital ingredient in proposed mechanisms ranging from psychological processes such as memory (24, 25, 26), attention (27, 28), to basic neural communication of a top-down and bottom-up type of information transfer (29,30,31,32,33,34,35,36).Recently, approaches to study brain connectomics and the dynamics of neuronal communication have started to merge. A significant amount of work has recently been carried out that aims to quantify dynamic fluctuations of network activity in the brain using fMRI (37,38,39,40,41,42) as well as MEG (7,43,9,44,35). This research area to unify brain connectommics with the dynamic properties of neuronal communication has been called the "dynome" (45) and the "chronnectome" (46). As the brain can quickly fluctuate between different tasks, the overarching aim of this area of research is to understand the dynamic interplay of the brain's networks. The intent of this research is that it will yield insight about the complex and dynamic cognitive human abilities.

Evolving Networks and Social Network Analysis Methods and Techniques

“…Spiliopoulou [28] enumerated the several challenges of the social network streams although this problem is generally conceived as a stream problem. An exciting application of temporal network theory and temporal networks to functional brain connectivity was presented by Thompson et al [29]; in his work, the theory and methods that introduce the reader on how to add the temporal dimension to network analysis and precisely how many of well-known methods can be transposed from static networks to temporal networks were presented. Thompson et al [29] included a complete list of network measures adapted or proposed for temporal networks.…”

“…Several models for representing evolving networks are available in the literature. Kim and Anderson [30] introduced the concept of a time-ordered graph, and Thompson et al [29] with a similar conceptual representation chose the time graphlet to represent time-varying graphs. Casteigts et al [31] presented the time-varying graph formalism (TVG) with the concept of a journey to catch the temporal information on graphs.…”

“…A hallmark of a bursty edge is the presence of multiple edges with short interconnect times, followed by longer and varying interconnect times [29]. One of the methods available to quantify bursts is the burstiness coefficient B.…”

“…As discussed before, centrality measures provide information about the degree of temporal connectivity while bursts describe the distribution of the temporal patterns of connectivity at the node level. Also, fluctuability can be used to retrieve information about the global state of a temporal network, in this case, the quantification of the temporal variability of connectivity [29]. The fluctuability F, as shown in (15), is the ratio of the number of edges present in A over the sum of A t ,wi thU being a function of the binary output: UA i, j ÀÁ is set to 1 if at least one of the edges occurs between nodes i and j across time t ¼ 1, 2, …,T and 0 if not.…”

“…The volatility V is a global measure of temporal order that represents how much, on an average, the connectivity between consecutive temporal time-ordered graphs changes [29]. This measure indicates how volatile the temporal network is over time and is computed by (17), where D is a distance function and T is the total number of time points.…”