Related papers: A Systematic Approach for Studying How Topological…
Comparing networks is essential for a number of downstream tasks, from clustering to anomaly detection. Despite higher-order interactions being critical for understanding the dynamics of complex systems, traditional approaches for network…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
The co-occurrence association is widely observed in many empirical data. Mining the information in co-occurrence data is essential for advancing our understanding of systems such as social networks, ecosystem, and brain network. Measuring…
Large-scale classification of data where classes are structurally organized in a hierarchy is an important area of research. Top-down approaches that exploit the hierarchy during the learning and prediction phase are efficient for large…
Modularity is designed to measure the strength of division of a network into clusters (known also as communities). Networks with high modularity have dense connections between the vertices within clusters but sparse connections between…
We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we…
In order to identify the extent to which results from topological graph models are useful for modeling vulnerability in electricity infrastructure, we measure the susceptibility of power networks to random failures and directed attacks…
We present a new approach to the calculation of measures in weighted networks, based on the translation of a weighted network into an ensemble of edges. This leads to a straightforward generalization of any measure defined on unweighted…
We review measures of street network structure proposed in the recent literature, establish their relevance to practice, and identify open challenges facing researchers. These measures' empirical values vary substantially across world…
Higher-order connectivity patterns such as small induced sub-graphs called graphlets (network motifs) are vital to understand the important components (modules/functional units) governing the configuration and behavior of complex networks.…
One of the most widely studied problem in mining and analysis of complex networks is the detection of community structures. The problem has been extensively studied by researchers due to its high utility and numerous applications in various…
Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multi-scale centrality in networks.…
We explore the geometry of complex networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian $(\bb L^+)$. The squared distance of a node $i$ to the origin in this…
A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behaviour. The inference process is often done by using bi-variate similarity measures, such as the…
The study of neuronal morphology is important not only for its potential relationship with neuronal dynamics, but also as a means to classify diverse types of cells and compare than among species, organs, and conditions. In the present…
Structural analysis in network science is finding the information hidden from the topology structure of complex networks. Many methods have already been proposed in the research on the structural analysis of complex networks to find the…
Turing instability in complex networks have been shown in the literature to be dominated by the distribution of the nodal degrees. The conditions for Turing instability have been derived with an explicit dependence on the eigenvalues of the…
This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the…
This letter deals with the controllability issue of complex networks. An index is chosen to quantitatively measure the extent of controllability of given network. The effect of this index is analyzed based on empirical studies on various…