Related papers: Distance Distribution in Extreme Modular Networks
In this work we study diffusion in networks with community structure. We first replicate and extend work on networks with non-overlapping community structure. We then study diffusion on network models that have overlapping community…
Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a…
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,…
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…
Modularity is one of the most prominent properties of real-world complex networks. Here, we address the issue of module identification in two important classes of networks: bipartite networks and directed unipartite networks. Nodes in…
This paper proposes a distributed pseudo-likelihood method (DPL) to conveniently identify the community structure of large-scale networks. Specifically, we first propose a block-wise splitting method to divide large-scale network data into…
We use the linear threshold model to study the diffusion of information on a network generated by the stochastic block model. We focus our analysis on a two community structure where the initial set of informed nodes lies only in one of the…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
Information dissemination is a fundamental and frequently occurring problem in large, dynamic, distributed systems. In order to solve this, there has been an increased interest in creating efficient overlay networks that can maintain…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
Complex network theory has shown success in understanding the emergent and collective behavior of complex systems [1]. Many real-world complex systems were recently discovered to be more accurately modeled as multiplex networks [2-6]---in…
The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…
A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for…
We propose a method to investigate modular structure in networks based on fitted probabilistic model, where the connection probability between nodes is related to a set of introduced local attributes. The attributes, as parameters of the…
We study high-density traffic of information packets on sparse modular networks with scale-free subgraphs. With different statistical measures we distinguish between the free flow and congested regime and point out the role of modules in…
Long range connections play an essential role in dynamical processes on networks, on the processing of information in biological networks, on the structure of social and economical networks and in the propagation of opinions and epidemics.…
We consider an infectious disease spreading along the edges of a network which may have significant clustering. The individuals in the population have heterogeneous infectiousness and/or susceptibility. We define the out-transmissibility of…
The shortest path multiplicity is an important metric of complex networks. The shortest path multiplicity of real networks is high and it correlates with their community structure. Since local network evolution induces network communities,…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…