Related papers: Extremal Properties of Complex Networks
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
Let $r(u,v)$ be the resistance distance between two vertices $u, v$ of a simple graph $G$, which is the effective resistance between the vertices in the corresponding electrical network constructed from $G$ by replacing each edge of $G$…
This note answers extremal questions like: what is the maximum number of edges in a graph of order n, which belongs to some hereditary property. The same question is answered also for the spectral radius and other similar parameters.
We systematically study a natural problem in extremal graph theory, to minimize the number of edges in a graph with a fixed number of vertices, subject to a certain local condition: each vertex must be in a copy of a fixed graph $H$. We…
Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…
Closeness is one of the most studied characteristics of networks. Residual closeness is a very sensitive measure of graphs robustness. Additional closeness is a measure of growth potentials of networks. In this article we calculate the…
A graph is trivial if it contains one vertex and no edges. The essential connectivity $\kappa^{\prime}$ of $G$ is defined to be the minimum number of vertices of $G$ whose removal produces a disconnected graph with at least two non-trivial…
Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy.…
Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years a multitude of diverse, ad hoc solutions to this problem have been introduced. Here we propose that simple and…
Many of the structural characteristics of a network depend on the connectivity with and within the hubs. These dependencies can be related to the degree of a node and the number of links that a node shares with nodes of higher degree. In…
Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these…
In this paper we explore maximal deviations of large random structures from their typical behavior. We introduce a model for a high-dimensional random graph process and ask analogous questions to those of Vapnik and Chervonenkis for…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Modularity is a key organizing principle in real-world large-scale complex networks. Many real-world networks exhibit modular structures such as transportation infrastructures, communication networks and social media. Having the knowledge…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
The structure entropy is an important index to illuminate the structure property of the complex network. Most of the existing structure entropies are based on the degree distribution of the complex network. But the structure entropy based…
Betweenness centrality is a centrality measure based on the overall amount of shortest paths passing through a given vertex. A graph is betweenness-uniform if all its vertices have the same betweenness centrality. We study the properties of…