Related papers: Network synchronizability analysis: the theory of …
Symmetries in a network regulate its organization into functional clustered states. Given a generic ensemble of nodes and a desirable cluster (or group of clusters), we exploit the direct connection between the elements of the eigenvector…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
Principal submatrices of the controllability Gramian and their inverses are examined, for a network-consensus model with inputs at a subset of network nodes. Specifically, several properties of the Gramian submatrices and their inverses --…
In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on…
As a quantification of the main bottleneck to flow over a graph, the network property of conductance plays an important role in the process of synchronization of network-coupled dynamical systems. Diffusive coupling terms serve not only to…
Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…
Symmetries in a network connectivity regulate how the graph's functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard,…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…
We describe SynGraphy, a method for visually summarising the structure of large network datasets that works by drawing smaller graphs generated to have similar structural properties to the input graphs. Visualising complex networks is…
The total graph is built by joining the graph to its line graph by means of the incidences. We introduce a similar construction for signed graphs. Under two similar definitions of the line signed graph, we define the corresponding total…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
The study of complex networks has been one of the most active fields in science in recent decades. Spectral properties of networks (or graphs that represent them) are of fundamental importance. Researchers have been investigating these…
Network topology inference is a prominent problem in Network Science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known, and then analyze how the graph's algebraic and spectral characteristics…
Hypergraphs have seen widespread application in network and data science communities in recent years. We present a survey of recent work to construct auxiliary structures from hypergraphs -- specifically simplicial, relative, and chain…
Scenarios elicit possibilities that may be ignored otherwise, as well as causal relations between them. Even when too little information is available to assess reliable probabilities, the structure of linkages between evoked alternatives…
Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of…
The growing popularity of dynamic applications such as social networks provides a promising way to detect valuable information in real time. Efficient analysis over high-speed data from dynamic applications is of great significance. Data…
In this article, we revisit and expand our prior work on graph similarity. As with our earlier work, we focus on a view of similarity which does not require node correspondence between graphs under comparison. Our work is suited to the…