相关论文: Average Path Length in Complex Networks: Patterns …
Many real world networks (graphs) are observed to be 'small worlds', i.e., the average path length among nodes is small. On the other hand, it is somewhat unclear what other average path length values networks can produce. In particular, it…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
Paths are important structural elements in complex networks because they are finite (unlike walks), related to effective node coverage (minimum spanning trees), and can be understood as being dual to star connectivity. This article…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
In this paper we present an analytic study of sampled networks in the case of some important shortest-path sampling models. We present analytic formulas for the probability of edge discovery in the case of an evolving and a static network…
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
Complex networks can be used to represent and model an ample diversity of abstract and real-world systems and structures. A good deal of the research on these structures has focused on specific topological properties, including node degree,…
Complex systems of interacting components often can be modeled by a simple graph $\mathcal{G}$ that consists of a set of $n$ nodes and a set of $m$ edges. Such a graph can be represented by an adjacency matrix $A\in\R^{n\times n}$, whose…
Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
Complex networks are graphs representing real-life systems that exhibit unique characteristics not found in purely regular or completely random graphs. The study of such systems is vital but challenging due to the complexity of the…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving…
Relations between average shortest path length and average clustering coefficient, radiality, closeness and stress centralities were obtained for simple graphs.
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the…
In a model of a connected network on random points in the plane, one expects that the mean length of the shortest route between vertices at distance $r$ apart should grow only as $O(r)$ as $r \to \infty$, but this is not always easy to…
This article explores the relationship between communities and short cycles in complex networks, based on the fact that nodes more densely connected amongst one another are more likely to be linked through short cycles. By identifying…
We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical…
Link prediction is an elemental challenge in network science, which has already found applications in guiding laboratorial experiments, digging out drug targets, recommending friends in social networks, probing mechanisms in network…