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The new concept of multilevel network is introduced in order to embody some topological properties of complex systems with structures in the mesoscale which are not completely captured by the classical models. This new model, which…
Understanding the complex hierarchical topology of functional brain networks is a key aspect of functional connectivity research. Such topics are obscured by the widespread use of sparse binary network models which are fundamentally…
We investigate degree correlations in two online social networks where users are connected through different types of links. We find that, while subnetworks in which links have a positive connotation, such as endorsement and trust, are…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…
We provide a general framework for analyzing degree correlations between nodes separated by more than one step (i.e., beyond nearest neighbors) in complex networks. One probability and four conditional probabilities are introduced to fully…
Centrality metrics aim to identify the most relevant nodes in a network. In literature, a broad set of metrics exists, either measuring local or global centrality characteristics. Nevertheless, when networks exhibit a high spectral gap, the…
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…
In complex networks there are overlapping substructures or "circles" that consist of nodes belonging to multiple cohesive subgroups. Yet the role of these overlapping nodes in influence spreading processes remains underexplored. In the…
Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this…
We report on exact results for the degree $K$, the diameter $D$, the clustering coefficient $C$, and the betweenness centrality $B$ of a hierarchical network model with a replication factor $M$. Such quantities are calculated exactly with…
Cycle is the simplest structure that brings redundant paths in network connectivity and feedback effects in network dynamics. Focusing on cycle structure, this paper defines a new matrix, named cycle number matrix, to represent cycle…
Spectral analysis of networks states that many structural properties of graphs, such as centrality of their nodes, are given in terms of their adjacency matrices. The natural extension of such spectral analysis to higher order networks is…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
Different types of graphs and complex networks have been characterized, analyzed, and modeled based on measurements of their respective topology. However, the available networks may constitute approximations of the original structure as a…
Several approaches to cognition and intelligence research rely on statistics-based models testing, namely factor analysis. In the present work we exploit the emerging dynamical systems perspective putting the focus on the role of the…
Knowledge silos emerge when structural properties of organizational interaction networks limit the diffusion of information. These structural barriers are known to take many forms at different scales - hubs in otherwise sparse…
Identifying the node spreading influence in networks is an important task to optimally use the network structure and ensure the more efficient spreading in information. In this paper, by taking into account the shortest distance between a…
Disease and information spread over social and information networks. Understanding the spread phenomena in networks requires paying attention not only to the degree distribution but also to the degree correlation. However, it is considered…
We compare the social character networks of biographical, legendary and fictional texts, in search for marks of genre differentiation. We examine the degree distribution of character appearance and find a power law that does not depend on…
Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it has been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The…