相关论文: Analytical results for the distribution of shortes…

We present analytical results for the distribution of shortest path lengths (DSPL) in a network growth model which evolves by node duplication (ND). The model captures essential properties of the structure and growth dynamics of social…

The distribution of shortest path lengths (DSPL) of random networks provides useful information on their large scale structure. In the special case of random regular graphs (RRGs), which consist of $N$ nodes of degree $c \ge 3$, the DSPL,…

In the subcritical regime Erd\H{o}s-R\'enyi (ER) networks consist of finite tree components, which are non-extensive in the network size. The distribution of shortest path lengths (DSPL) of subcritical ER networks was recently calculated…

We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to…

We present exact results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific…

In a network, the shortest paths between nodes are of great importance as they allow the fastest and strongest interaction between nodes. However measuring the shortest paths between all nodes in a large network is computationally…

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…

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…

We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-R\'enyi networks, based on recursion equations for the shells around a reference node and for the paths originating from…

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…

Given a network infrastructure (e.g., data-center or on-chip-network) and a distribution on the source-destination requests, the expected path (route) length is an important measure for the performance, efficiency and power consumption of…

We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…

Self-paced learning (SPL) mimics the cognitive process of humans, who generally learn from easy samples to hard ones. One key issue in SPL is the training process required for each instance weight depends on the other samples and thus…

In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large…

Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed counting questions for bicombining tree-child networks in which…

A network topology with low average shortest path length (ASPL) provides efficient data transmission while the number of nodes and the number of links incident to each node are often limited due to physical constraints. In this paper, we…

We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…

Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…

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…

Spreading according to simple rules (e.g. of fire or diseases), and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connections (``Small-World'' lattices). The volume V(t) covered…