Dynamics of and on Networks
Virtually any network is a dynamic entity. New nodes arrive, others leave, connections are created and renewed in time subject to complex temporal dynamics. However, initially due to the lack of time-resolved data and later to the mathematical challenges that time introduces, the large majority of results, models, and approaches developed by Network Scientists neglect time in favor of time-aggregated descriptions. This approximation is useful and appropriate in some systems and processes, but it fails in many others. For example, in the case of sexually transmitted diseases, ideas, cyber threats, and meme spreading, the co-occurrence, duration, and order of contacts are crucial ingredients. The importance and relevance of this limit have become clearer as we gained access also to the temporal information of many systems. However, our understanding of it is still far from complete.
In 2012, I developed the activity-driven modeling framework to describe highly dynamical networks [1]. Since then, the framework has become popular in the area of time-varying networks. I have largely extended the initial model to account for more realistic links' creation dynamics such as the presence of i) weak/strong ties [2], ii) communities [3], iii) popularity [4], iv) burstiness [5] v) context dependent features [6]. Furthermore, I extended the model from mono-plexes (i.e., single isolated networks) to multi-plexes (i.e., networks in which connections disentangled multiple plexes/contexts) [7]. Besides the challenge to develop more and more realistic models, I used the framework as vantage point to understand the role of temporal connectivity patterns on a range of processes such as random walks [4, 8, 9], epidemics [1, 2, 3], complex contagion [8], cyber threats [9] and reaction-diffusion processes [10].
I am currently exploring four different new directions in this research area. First, the activity-driven framework so far does not allow to capture, at least explicitly, high-order structural and temporal correlations. Accounting for these complex dynamics is key to moving towards more realistic time-varying network models. Second, with few exceptions, the study of dynamical processes on time-varying networks has been largely limited to simple (i.e., biological) contagion processes. However, social norms, (mis)information, beliefs, and innovations diffuse through social networks via complex contagion processes. Third, visualizing networks is a very hard task. As result, temporal networks are typically described by integrating links over time. In some cases, animated sequences of networks (where links are integrated into small temporal windows) can be used. However, they are rarely able to provide any real insights. Fundamental and theoretical work is needed to understand how to capture and encode the evolution of networks. To this end, understanding and modeling the high-order dynamics of the systems under study might provide new tools to summarize temporal connectivity patterns. Fourth, centrality measures have been crucial in networks, and provide us with efficient control and searching strategies. However, so far all the proposed quantities in the context of temporal networks have been simple extensions of existing measures created for static or annealed systems. Surprisingly, a novel centrality measure designed specifically for capturing the basic characteristics of time-varying networks is still missing.
In 2012, I developed the activity-driven modeling framework to describe highly dynamical networks [1]. Since then, the framework has become popular in the area of time-varying networks. I have largely extended the initial model to account for more realistic links' creation dynamics such as the presence of i) weak/strong ties [2], ii) communities [3], iii) popularity [4], iv) burstiness [5] v) context dependent features [6]. Furthermore, I extended the model from mono-plexes (i.e., single isolated networks) to multi-plexes (i.e., networks in which connections disentangled multiple plexes/contexts) [7]. Besides the challenge to develop more and more realistic models, I used the framework as vantage point to understand the role of temporal connectivity patterns on a range of processes such as random walks [4, 8, 9], epidemics [1, 2, 3], complex contagion [8], cyber threats [9] and reaction-diffusion processes [10].
I am currently exploring four different new directions in this research area. First, the activity-driven framework so far does not allow to capture, at least explicitly, high-order structural and temporal correlations. Accounting for these complex dynamics is key to moving towards more realistic time-varying network models. Second, with few exceptions, the study of dynamical processes on time-varying networks has been largely limited to simple (i.e., biological) contagion processes. However, social norms, (mis)information, beliefs, and innovations diffuse through social networks via complex contagion processes. Third, visualizing networks is a very hard task. As result, temporal networks are typically described by integrating links over time. In some cases, animated sequences of networks (where links are integrated into small temporal windows) can be used. However, they are rarely able to provide any real insights. Fundamental and theoretical work is needed to understand how to capture and encode the evolution of networks. To this end, understanding and modeling the high-order dynamics of the systems under study might provide new tools to summarize temporal connectivity patterns. Fourth, centrality measures have been crucial in networks, and provide us with efficient control and searching strategies. However, so far all the proposed quantities in the context of temporal networks have been simple extensions of existing measures created for static or annealed systems. Surprisingly, a novel centrality measure designed specifically for capturing the basic characteristics of time-varying networks is still missing.
