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Networks are known to be prone to link failures. In this paper we set out to investigate how networks of varying connectivity patterns respond to different link failure schemes in terms of connectivity, clustering coefficient and shortest…
Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…
We use the configuration model to generate networks having a degree distribution that follows a $q$-exponential, $P_q(k)=(2-q)\lambda[1-(1-q)\lambda k]^{1/(q-1)}$, for arbitrary values of the parameters $q$ and $\lambda$. We study the…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment…
We study fully synchronized states in scale-free networks of chaotic logistic maps as a function of both dynamical and topological parameters. Three different network topologies are considered: (i) random scale-free topology, (ii)…
In heterogeneous network systems such as ecological and social networks, structural stability depends on how connectivity changes under node removal, as different removal sequences can trigger distinct modes of systemic collapse. While…
Many real networks present a bounded scale-free behavior with a connectivity cut-off due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cut-offs.…
The size and number of maximum matchings in a network have found a large variety of applications in many fields. As a ubiquitous property of diverse real systems, power-law degree distribution was shown to have a profound influence on size…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
Real-life networks often encounter vertex dysfunctions, which are usually followed by recoveries after appropriate maintenances. In this paper we present our research on a model of scale-free networks whose vertices are regularly removed…
We present a detailed analytical and numerical study for the spreading of infections in complex population networks with acquired immunity. We show that the large connectivity fluctuations usually found in these networks strengthen…
Complex networks have abundant and extensive applications in real life. Recently, researchers have proposed a number of complex networks, in which some are deterministic and others are random. Compared with deterministic networks, random…
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…