Related papers: Bipartite Graphs as Models of Complex Networks
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
Finding community structures in networks is important in network science, technology, and applications. To date, most algorithms that aim to find community structures only focus either on unipartite or bipartite networks. A unipartite…
The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph G is distance-regular if and only if its spectral excess (a number that can be…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…
Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
Bipartite (two-mode) networks are important in the analysis of social and economic systems as they explicitly show conceptual links between different types of entities. However, applications of such networks often work with a projected…
The study of complex networks is a significant development in modern science, and has enriched the social sciences, biology, physics, and computer science. Models and algorithms for such networks are pervasive in our society, and impact…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…