Related papers: Network Entropy based on Cluster Expansion on Moti…
In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at…
Real-world networks are often organized as modules or communities of similar nodes that serve as functional units. These networks are also rich in content, with nodes having distinguishing features or attributes. In order to discover a…
We propose a method of characterizing radial networks based on a partition function associated with the structural triangulation of the network. The internal energy, Helmholtz free energy, and entropy derived from the partition function are…
Graph mining to extract interesting components has been studied in various guises, e.g., communities, dense subgraphs, cliques. However, most existing works are based on notions of frequency and connectivity and do not capture subjective…
How does the small-scale topological structure of an airline network behave as the network evolves? To address this question, we study the dynamic properties of small undirected subgraphs using 15 years of data on Southwest Airlines'…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. Clustering, community structure and assortative mixing by degree are perhaps among most prominent…
In this paper we generalize the concept of random networks to describe networks with non trivial features by a statistical mechanics approach. This framework is able to describe ensembles of undirected, directed as well as weighted…
Interaction networks are of central importance in post-genomic molecular biology, with increasing amounts of data becoming available by high-throughput methods. Examples are gene regulatory networks or protein interaction maps. The main…
We study the applicability of a set of texture descriptors introduced in recent work by the author to texture-based segmentation of images. The texture descriptors under investigation result from applying graph indices from quantitative…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
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.…
The idea underlying the modal formulation of density-based clustering is to associate groups with the regions around the modes of the probability density function underlying the data. This correspondence between clusters and dense regions…
We introduce a method to convert an ensemble of sequences of symbols into a weighted directed network whose nodes are motifs, while the directed links and their weights are defined from statistically significant co-occurences of two motifs…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
We present a novel graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of "motif-hubs" (multiple overlapping significant…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…