Related papers: On proportional network connectivity
Measurement has become fundamental to the operation of networks and at-scale services---whether for management, security, diagnostics, optimization, or simply enhancing our collective understanding of the Internet as a complex system.…
In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are…
Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the…
Let \( G \) be a finite simple undirected graph. Four graph parameters related to network monitoring are the \emph{geodetic set}, \emph{edge geodetic set}, \emph{strong edge geodetic set}, and \emph{monitoring edge geodetic set}, with…
A bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components. We calculate the fraction of bridges in a wide range of real-world networks and their randomized counterparts. We find that…
Network coding theory studies the transmission of information in networks whose vertices may perform nontrivial encoding and decoding operations on data as it passes through the network. The main approach to deciding the feasibility of…
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…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
The approach of quantifying the damage inflicted on a graph in Albert, Jeong and Barabsi's (AJB) report "Error and Attack Tolerance of Complex Networks" using the size of the largest connected component and the average size of the remaining…
Robustness of ecological flow networks under random failure of arcs is considered with respect to two different functionalities: coherence and circulation. In our previous work, we showed that each functionality is associated with a natural…
Network controllability measures how well a networked system can be controlled to a target state, and its robustness reflects how well the system can maintain the controllability against malicious attacks by means of node-removals or…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks…
We provide a method for the ranking of the reliability of two networks with the same connectance. Our method is based on the Cheeger constant linking the topological property of a network with its spectrum. We first analyze a set of twisted…
We study the robustness of complex networks subject to edge removal. Several network models and removing strategies are simulated. Rather than the existence of the giant component, we use total connectedness as the criterion of breakdown.…
Structural balance theory predicts that triads in networks gravitate towards stable configurations. The theory has been verified for undirected graphs. Since real-world networks are often directed, we introduce a novel method for…
A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some necessary and some sufficient conditions on the sizes of the…
We investigate robustness of correlated networks against propagating attacks modeled by a susceptible-infected-removed model. By Monte-Carlo simulations, we numerically determine the first critical infection rate, above which a global…
We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…