Related papers: Small-world networks and RNA secondary structures
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
Small-worlds represent efficient communication networks that obey two distinguishing characteristics: a high clustering coefficient together with a small characteristic path length. This paper focuses on an interesting paradox, that…
Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…
We reformulated the string formalism given by Aoyama, using an adjacent matrix of a network and introduced a series of generalized clustering coefficients based on it. Furthermore we numerically evaluated Milgram condition proposed by their…
Random scale-free networks have the peculiar property of being prone to the spreading of infections. Here we provide an exact result showing that a scale-free connectivity distribution with diverging second moment is a sufficient condition…
Networks that are fragmented into small disconnected components are prevalent in a large variety of systems. These include the secure communication networks of commercial enterprises, government agencies and illicit organizations, as well…
This paper studies the enumeration of seven subclasses of level-$2$ phylogenetic networks under various planarity and structural constraints, including terminal planar, tree-child, and galled networks. We derive their exponential generating…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
A model for the spread of an infection is analyzed for different population structures. The interactions within the population are described by small world networks, ranging from ordered lattices to random graphs. For the more ordered…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behaviour. The inference process is often done by using bi-variate similarity measures, such as the…
We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity and as well as the full spectrum distribution.…
We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…
Large bibliographic networks are sparse -- the average node degree is small. This is not necessarily true for their product -- in some cases, it can ``explode'' (it is not sparse, increases in time and space complexity). An approach in such…
Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…
The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…
The clustering property of complex networks indicates the abundance of small dense subgraphs in otherwise sparse networks. For a community-affiliation network defined by a superposition of Bernoulli random graphs, which has a nonvanishing…
Let A be a minor-closed class of labelled graphs, and let G_n be a random graph sampled uniformly from the set of n-vertex graphs of A. When n is large, what is the probability that G_n is connected? How many components does it have? How…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
We apply complex network analysis to the state spaces of random Boolean networks (RBNs). An RBN contains $N$ Boolean elements each with $K$ inputs. A directed state space network (SSN) is constructed by linking each dynamical state,…