Related papers: A spectral graph theoretic study of predator-prey …
We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural…
Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…
Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
A power law degree distribution is established for a graph evolution model based on the graph class of k-trees. This k-tree-based graph process can be viewed as an idealized model that captures some characteristics of the preferential…
Recent developments in graph theoretic analysis of complex networks have led to deeper understanding of brain networks. Many complex networks show similar macroscopic behaviors despite differences in the microscopic details. Probably two…
Graphs are naturally used to describe the structures of various real-world systems in biology, society, computer science etc., where subgraphs or motifs as basic blocks play an important role in function expression and information…
Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…
Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is…
We consider a statistical model for the problem of finding subgraphs with specified topology in an otherwise random graph. This task plays an important role in the analysis of social and biological networks. In these types of networks,…
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
In this paper, we describe {\sc quantitative graph theory} and argue it is a new graph-theoretical branch in network science, however, with significant different features compared to classical graph theory. The main goal of quantitative…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
In this paper, a new measurement to compare two large-scale graphs based on the theory of quantum probability is proposed. An explicit form for the spectral distribution of the corresponding adjacency matrix of a graph is established. Our…
In this paper we study self-similar and fractal networks from the combinatorial perspective. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring…