Related papers: A geometry-induced topological phase transition in…
Finding densely connected subsets of vertices in an unsupervised setting, called clustering or community detection, is one of the fundamental problems in network science. The edge clustering approach instead detects communities by…
In Network Science node neighbourhoods, also called ego-centered networks have attracted large attention. In particular the clustering coefficient has been extensively used to measure their local cohesiveness. In this paper, we show how,…
We report on a hitherto unnoticed type of resonances occurring in scattering from networks (quantum graphs) which are due to the complex connectivity of the graph - its topology. We consider generic open graphs and show that any cycle leads…
The exponential family of random graphs is one of the most promising class of network models. Dependence between the random edges is defined through certain finite subgraphs, analogous to the use of potential energy to provide dependence…
Networks of companies can be constructed by using return correlations. A crucial issue in this approach is to select the relevant correlations from the correlation matrix. In order to study this problem, we start from an empty graph with no…
A new point of view about the deep origin of thermodynamic phase transitions is sketched. The main idea is to link the appearance of phase transitions to some major topology change of suitable submanifolds of phase space instead of linking…
The giant $k$-core --- maximal connected subgraph of a network where each node has at least $k$ neighbors --- is important in the study of phase transitions and in applications of network theory. Unlike Erd\H{o}s-R\'enyi graphs and other…
We introduce and study systems of randomly coupled maps (RCM) where the relevant parameter is the degree of connectivity in the system. Global (almost-) synchronized states are found (equivalent to the synchronization observed in globally…
Community structures have been identified in various complex real-world networks, for example, communication, information, internet and shareholder networks. The scaling of community size distribution indicates the heterogeneity in the…
Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed - in the sense that there is directionality on…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent…
Clustering is indispensable for data analysis in many scientific disciplines. Detecting clusters from heavy noise remains challenging, particularly for high-dimensional sparse data. Based on graph-theoretic framework, the present paper…
The ground states of noninteracting fermions in one-dimension with chiral symmetry form a class of topological band insulators, described by a topological invariant that can be related to the Zak phase. Recently, a generalization of this…
Many real networks can be understood as two complementary networks with two kind of nodes. This is the case of metabolic networks where the first network has chemical compounds as nodes and the second one has nodes as reactions. The second…
Simplicial complexes capture the underlying network topology and geometry of complex systems ranging from the brain to social networks. Here we show that algebraic topology is a fundamental tool to capture the higher-order dynamics of…
Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. In order to compute the various topological descriptors commonly used to characterize the structure of…
Recent empirical observations suggest that network transitivity is highly correlated with community structure in many real-world networks. In this paper, we theoretically investigate this relationship by deriving the limits of the global…