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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...
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Many real-world systems are profitably described as complex networks that grow over time. Preferential attachment and node fitness are two simple growth mechanisms that not only explain certain structural properties commonly observed in real-world systems, but are also tied to a number of applications in modeling and inference. While there are stat...
The preferential attachment model is a natural and popular random graph model for a growing network that contains very well-connected ``hubs''. We study the higher-order connectivity of such a network by investigating the topological properties of its clique complex. We concentrate on the expected Betti numbers, a sequence of topological invariants...
Many real-world systems are profitably described as complex networks that grow over time. Preferential attachment and node fitness are two simple growth mechanisms that not only explain certain structural properties commonly observed in real-world systems, but are also tied to a number of applications in modeling and inference. While there are stat...
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... Also, Wu et al. [20] have recently proposed a simplicial complex generation model but with a significantly different goal of characterizing the growing geometry of networks. Very recently, growth models for collaboration artifacts have been considered [13], but they address neither the success of matching the size distribution nor subsumption phenomena, which is a focal point of this paper. ...
... with f cld (u) obtained through (13). Here we note that while modifying standard PA has been considered in [21], which propose a nonlinear preferential attachment by replacing node degree f d (u) by f d (u) β for each node in the connection process with some given β , our clamped PA defined by the mapping in (13) is significantly different and also depends on many distinct parameters as α and f max d . ...
When individuals interact with each other and meaningfully contribute toward a common goal, it results in a collaboration, as can be seen in many walks of life such as scientific research, motion picture production, or team sports. The artifacts resulting from a collaboration (e.g. papers, movies) are best captured using a hypergraph model, whereas the relation of who has collaborated with whom is best captured via an abstract simplicial complex (SC). In this paper, we propose a generative algorithm GeneSCs for SCs modeling fundamental collaboration relations, primarily based on preferential attachment. The proposed network growth process favors attachment that is preferential not to an individual's degree, i.e., how many people has he/she collaborated with, but to his/her facet degree, i.e., how many maximal groups or facets has he/she collaborated within. Unlike graphs, in SCs, both facet degrees (of nodes) and facet sizes are important to capture connectivity properties. Based on our observation that several real-world facet size distributions have significant deviation from power law-mainly due to the fact that larger facets tend to subsume smaller ones-we adopt a data-driven approach. We seed GeneSCs with a facet size distribution informed by collaboration network data and randomly grow the SC facet-by-facet to generate a final SC whose facet degree distribution matches real data. We prove that the facet degree distribution yielded by GeneSCs is power law distributed for large SCs and show that it is in agreement with real world co-authorship data. Finally, based on our intuition of collaboration formation in domains such as collaborative scientific experiments and movie production, we propose two variants of GeneSCs based on clamped and hybrid preferential attachment schemes, and show that they perform well in these domains.
... Also, Wu et al. [20] have recently proposed a simplicial complex generation model but with a significantly different goal of characterizing the growing geometry of networks. Very recently, growth models for collaboration artifacts have been considered [13], but they address neither the success of matching the size distribution nor subsumption phenomena, which is a focal point of this paper. ...
... with f cld (u) obtained through (13). Here we note that while modifying standard PA has been considered in [21], which propose a nonlinear preferential attachment by replacing node degree f d (u) by f d (u) β for each node in the connection process with some given β , our clamped PA defined by the mapping in (13) is significantly different and also depends on many distinct parameters as α and f max d . ...
When individuals interact with each other and meaningfully contribute toward a common goal, it results in a collaboration, as can be seen in many walks of life such as scientific research, motion picture production, or team sports. The artifacts resulting from a collaboration (e.g. papers, movies) are best captured using a hypergraph model, whereas the relation of who has collaborated with whom is best captured via an abstract simplicial complex (SC). In this paper, we propose a generative algorithm GeneSCs for SCs modeling fundamental collaboration relations, primarily based on preferential attachment. The proposed network growth process favors attachment that is preferential not to an individual's degree, i.e., how many people has he/she collaborated with, but to his/her facet degree, i.e., how many maximal groups or facets has he/she collaborated within. Unlike graphs, in SCs, both facet degrees (of nodes) and facet sizes are important to capture connectivity properties. Based on our observation that several real-world facet size distributions have significant deviation from power law-mainly due to the fact that larger facets tend to subsume smaller ones-we adopt a data-driven approach. We seed GeneSCs with a facet size distribution informed by collaboration network data and randomly grow the SC facet-by-facet to generate a final SC whose facet degree distribution matches real data. We prove that the facet degree distribution yielded by GeneSCs is power law distributed for large SCs and show that it is in agreement with real world co-authorship data. Finally, based on our intuition of collaboration formation in domains such as collaborative scientific experiments and movie production, we propose two variants of GeneSCs based on clamped and hybrid preferential attachment schemes, and show that they perform well in these domains.
Using the headers of scientific papers, we have built multilayer networks of entities involved in research namely: authors, laboratories, and institutions. We have analyzed some properties of such networks built from data extracted from the HAL archives and found that the network at each layer is a small-world network with power law distribution. In order to simulate such co-publication network, we propose a multilayer network generation model based on the formation of cliques at each layer and the affiliation of each new node to the higher layers. The clique is built from new and existing nodes selected using preferential attachment. We also show that, the degree distribution of generated layers follows a power law. From the simulations of our model, we show that the generated multilayer networks reproduce the studied properties of co-publication networks.
