Abstract
We propose a model of growing networks based on cliques formations. A clique is used to illustrate for example co-authorship in co-publication networks, co-occurence of words or collaboration between actors of the same movie. Our model is iterative and at each step, a clique of λη existing vertices and (1 − λ)η new vertices is created and added in the network; η is the mean number of vertices per clique and λ is the proportion of old vertices per clique. The old vertices are selected according to preferential attachment. We show that the degree distribution of the generated networks follows the Power Law of parameter 1 + 1/ λ and thus they are ultra small-world networks with high clustering coefficient and low density. Moreover, the networks generated by the proposed model match with some real co-publication networks such as CARI, EGC and HepTh. Nous proposons un modèle de croissance de graphe basé sur la formation de clique. Une clique peut par exemple illustrer la collaboration entre auteurs dans un réseau de co-publication, les relations de co-occurrence des mots dans une phrase ou les relations entre acteurs d'un film. C'est un modèle itératif qui à chaque étape crée une clique de λη anciens sommets et (1 − λ)η nouveaux sommets et l'insère dans le graphe. η est le nombre moyen de sommets dans une clique et λ la proportion moyenne d'anciens sommets dans une clique. La distribution des degrés des réseaux générés suit la Loi de Puissance de paramètre 1 + 1/λ et par conséquent ce sont des réseaux petit-mondes qui présentent un coefficient de clustering élevé et une faible densité. En outre, les réseaux générés par le modèle proposé reproduisent la structure des réseaux de terrains à l'instar des réseaux de co-publication du CARI, de EGC et de HepTh.
Highlights
In many application contexts, we encounter large graphs with no apparent simple structure named real networks
It appeared that the classical random graph model used to represent real-world complex networks does not capture their main properties [12]
An alternative definition of the transitivity is the clustering coefficient,wich has been given by Watts and Strogatz [6], who proposed to define a local value of transitivity in each vertex; the clustering coefficient for the whole network is the average of those local transitivity
Summary
We encounter large graphs with no apparent simple structure named real networks. A social network is a set of people or groups of people with some pattern of contacts or interactions between them It appeared that the classical random graph model used to represent real-world complex networks does not capture their main properties [12]. Real networks have a very low density, an average short distance, a degree distribution that follows the Power Law, a high clustering coefficient and high transitivity [12, 17]. We propose in this paper a new way, both simple and realistic, for reproducing these characteristics Real networks such as co-publication networks have short average distances, low densities, Power law distribution and high clustering coefficients.
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