Related papers: Characterizing the structure of small-world networ…
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…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
Various types of walks on complex networks have been used in recent years to model search and navigation in several kinds of systems, with particular emphasis on random walks. This gives valuable information on network properties, but…
We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With…
A wealth of evidence shows that real world networks are endowed with the small-world property i.e., that the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. In addition, most…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
Statistical properties of position-dependent ball-passing networks in real football games are examined. We find that the networks have the small-world property, and their degree distributions are fitted well by a truncated gamma…
Small-world networks, known for high local clustering and short path lengths, are a fundamental structure in many real-world systems, including social, biological, and technological networks. We apply the theory of (marked) local…
In this work we investigate the dynamics of random walk processes on scale-free networks in a short to moderate time scale. We perform extensive simulations for the calculation of the mean squared displacement, the network coverage and the…
Stanley Milgram's small world experiment presents "six degrees of separation" of our world. One phenomenon of the experiment still puzzling us is that how individuals operating with the social network information with their characteristics…
Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these…
A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…
Many social and biological networks consist of communities - groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting…
Many real-world networks have properties of small-world networks, with clustered local neighborhoods and low average-shortest path (ASP). They may also show a scale-free degree distribution, which can be generated by growth and preferential…
We investigate the dynamics of random walks on weighted networks. Assuming that the edge's weight and the node's strength are used as local information by a random walker, we study two kinds of walks, weight-dependent walk and…
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…
To comprehend the hierarchical organization of large integrated systems, we introduce the hierarchical map equation, which reveals multilevel structures in networks. In this information-theoretic approach, we exploit the duality between…
The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as…
We present scaling laws that dictate both local and global connectivity properties of bounded wireless networks. These laws are defined with respect to the key system parameters of per-node transmit power and the number of antennas…
We use scaling results to identify the crossover to mean-field behavior of equilibrium statistical mechanics models on a variant of the small world network. The results are generalizable to a wide-range of equilibrium systems. Anomalous…