Related papers: Network Cosmology
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
The topology of any complex system is key to understanding its structure and function. Fundamentally, algebraic topology guarantees that any system represented by a network can be understood through its closed paths. The length of each path…
The universal symmetry, or conservation, of complexity underlies any law or principle of system dynamics and describes the unceasing transformation of dynamic information into dynamic entropy as the unique way to conserve their sum, the…
The Internet is the most complex system ever created in human history. Therefore, its dynamics and traffic unsurprisingly take on a rich variety of complex dynamics, self-organization, and other phenomena that have been researched for…
The connectivity of a network contains information about the relationships between nodes, which can denote interactions, associations, or dependencies. We show that this information can be analyzed by measuring the uncertainty (and…
We introduce a novel tool for analyzing complex network dynamics, allowing for cascades of causally-related events, which we call causal webs (c-webs), to be separated from other non-causally-related events. This tool shows that…
In continuation of prior work, we investigate ties between a network's connectivity and ensemble dynamics. This relationship is notoriously difficult to approach mathematically in natural, complex networks. In our work, we aim to understand…
Links in most real networks often change over time. Such temporality of links encodes the ordering and causality of interactions between nodes and has a profound effect on network dynamics and function. Empirical evidences have shown that…
Graph or network representations are an important foundation for data mining and machine learning tasks in relational data. Many tools of network analysis, like centrality measures, information ranking, or cluster detection rest on the…
The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a…
One important question in neuroscience is how global behavior in a brain network emerges from the interplay between network connectivity and the neural dynamics of individual nodes. To better understand this theoretical relationship, we…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust…
A common feature of biological networks is the geometric property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks, show self-similar…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely,…
We study the emergence of coherence in complex networks of mutually coupled non-identical elements. We uncover the precise dependence of the dynamical coherence on the network connectivity, on the isolated dynamics of the elements and the…
Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for…
Our ability to manipulate the behavior of complex networks depends on the design of efficient control algorithms and, critically, on the availability of an accurate and tractable model of the network dynamics. While the design of control…
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…