Related papers: Assortative Mixing in Close-Packed Spatial Network…

In multiplex networks, cycles cannot be characterized only by their length, as edges may occur in different layers in different combinations. We define a classification of cycles by the number of edges in each layer and the number of…

We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…

Assortativity was first introduced by Newman and has been extensively studied and applied to many real world networked systems since then. Assortativity is a graph metrics and describes the tendency of high degree nodes to be directly…

The concept of nestedness, in particular for ecological and economical networks, has been introduced as a structural characteristic of real interacting systems. We suggest that the nestedness is in fact another way to express a mesoscale…

The random networks enriched with additional structures as metric and group-symmetry in background metric space are investigated. The important quantities like he clustering coefficient as well as the mean degree of separation in such…

We study the influence of degree correlations or network mixing in interdependent security. We model the interdependence in security among agents using a dependence graph and employ a population game model to capture the interaction among…

Network classification aims to group networks (or graphs) into distinct categories based on their structure. We study the connection between classification of a network and of its constituent nodes, and whether nodes from networks in…

Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…

Network science plays an increasingly important role to model complex data in many scientific disciplines. One notable feature of network organization is community structure, which refers to clusters of tightly interconnected nodes. A…

In principle, the rules of links formation of a network model can be considered as a kind of link prediction algorithm. By revisiting the preferential attachment mechanism for generating a scale-free network, here we propose a class of…

The analysis of the activity of neuronal cultures is considered to be a good proxy of the functional connectivity of in vivo neuronal tissues. Thus, the functional complex network inferred from activity patterns is a promising way to…

In this paper, we study the role of degree mixing in the naming game. It is found that consensus can be accelerated on disassortative networks. We provide a qualitative explanation of this phenomenon based on clusters statistics. Compared…

A useful property of a network that can be used to characterize many systems is the degree distribution. However, many complex networks exhibit higher--order degree correlations that must be studied through other means, such as clustering…

Heterogeneity is a key aspect of complex networks, often emerging by looking at the distribution of node properties, from the milestone observations on the degree to the recent developments in mixing pattern estimation. Mixing patterns, in…

Nearest-neighbor methods are fundamental to classical and modern machine learning, yet their geometric properties are typically analyzed under independent sampling. In this paper, we study the nearest-neighbor radii under dependent…

A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…

Multilevel self-assembly involving small structured groups of nano-particles provides new routes to development of functional materials with a sophisticated architecture. Apart from the inter-particle forces, the geometrical shapes and…

The studies based on $A+A \rightarrow \emptyset$ and $A+B\rightarrow \emptyset$ diffusion-annihilation processes have so far been studied on weighted uncorrelated scale-free networks and fractal scale-free networks. In the previous reports,…

Nestedness characterizes the linkage pattern of networked systems, indicating the likelihood that a node is linked to the nodes linked to the nodes with larger degrees than it. Networks of mutualistic relationship between distinct groups of…

Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current…