Related papers: Are Barabasi-Albert networks self-averaging?
In this article we present a new centrality measure called ksi-centrality. We show that ksi-centrality distinguishes real networks from random ones, similar to degree centrality: the ksi-centrality distribution is right-skewed for real…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
With a simple attack and repair evolution model, we investigate the stability and structural changes of the Erdos-Renyi random graphs (RG) and Barabasi-Albert scale-free (SF) networks. We introduce a new quantity, invulnerability I(s), to…
Activity or spin patterns on random scale-free network are studied by mean field analysis and computer simulations. These activity patterns evolve in time according to local majority-rule dynamics which is implemented using (i) parallel or…
Inspired by the importance of inhibitory and excitatory couplings in the brain, we analyze the largest eigenvalue statistics of random networks incorporating such features. We find that the largest real part of eigenvalues of a network,…
A population of complete subgraphs or cliques in a network evolving via duplication-divergence is considered. We find that a number of cliques of each size scales linearly with the size of the network. We also derive a clique population…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
A central claim in modern network science is that real-world networks are typically "scale free," meaning that the fraction of nodes with degree $k$ follows a power law, decaying like $k^{-\alpha}$, often with $2 < \alpha < 3$. However,…
The consensus model of Deffuant et al is simplified by allowing for many discrete instead of infinitely many continuous opinions, on a directed Barabasi-Albert network. A simple scaling law is observed. We then introduce noise and also use…
We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network…
Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as…
It is becoming more and more clear that complex networks present remarkable large fluctuations. These fluctuations may manifest differently according to the given model. In this paper we re-consider hidden variable models which turn out to…
Many real-world networks display a natural bipartite structure. Investigating it based on the original structure is helpful to get deep understanding about the networks. In this paper, some real-world bipartite networks are collected and…
Multilayer networks are widespread in natural and manmade systems. Key properties of these networks are their spectral and eigenfunction characteristics, as they determine the critical properties of many dynamics occurring on top of them.…
Isolated complex networks have been studied deeply in the last decades due to the fact that many real systems can be modeled using these types of structures. However, it is well known that the behavior of a system not only depends on…
We analyze eigenvalues fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that nearest neighbor spacing distribution of…
We define a statistical ensemble of non-degenerate graphs, i.e. graphs without multiple- and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier…
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…
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…
Many real-world networks are large, complex and thus hard to understand, analyze or visualize. The data about networks is not always complete, their structure may be hidden or they change quickly over time. Therefore, understanding how…