Related papers: Subsuming Complex Networks by Node Walks
Recently, some studies started to unveil the wealthy of interactions that occur between groups of nodes when looking at the small scale of interactions taking place in complex networks. Such findings claim for a new systematic methodology…
We introduce the concept of network susceptibilities quantifying the response of the collective dy- namics of a network to small parameter changes. We distinguish two types of susceptibilities: vertex susceptibilities and edge…
Many social, technological, biological, and economical systems are best described by weighted networks, whose properties and dynamics depend not only on their structures but also on the connection weights among their nodes. However, most…
In network science complex systems are represented as a mathematical graphs consisting of a set of nodes representing the components and a set of edges representing their interactions. The framework of networks has led to significant…
Several kinds of walks on complex networks are currently used to analyze search and navigation in different systems. Many analytical and computational results are known for random walks on such networks. Self-avoiding walks (SAWs) are…
When dealing with large graphs, such as those that arise in the context of online social networks, a subset of nodes may be labeled. These labels can indicate demographic values, interest, beliefs or other characteristics of the nodes…
This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the…
Many real-world applications give rise to large heterogeneous networks where nodes and edges can be of any arbitrary type (e.g., user, web page, location). Special cases of such heterogeneous graphs include homogeneous graphs, bipartite,…
We study the extreme events taking place on complex networks. The transport on networks is modelled using random walks and we compute the probability for the occurance and recurrence of extreme events on the network. We show that the nodes…
Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…
Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…
Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in…
We present a simple mathematical framework for the description of the dynamics of glassy systems in terms of a random walk in a complex energy landscape pictured as a network of minima. We show how to use the tools developed for the study…
Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…
The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
In the last two decades we are witnessing a huge increase of valuable big data structured in the form of graphs or networks. To apply traditional machine learning and data analytic techniques to such data it is necessary to transform graphs…
We consider distributed networks, such as peer-to-peer networks, whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
Our goal is to quickly find top $k$ lists of nodes with the largest degrees in large complex networks. If the adjacency list of the network is known (not often the case in complex networks), a deterministic algorithm to find a node with the…