A limitation of the Graph Convolutional Networks (GCNs) is that it assumes at a particular @math layer of the neural network model only the @math order neighbourhood nodes of a social network are influential. Furthermore, the GCN has been evaluated on citation and knowledge graphs, but not extensively on friendship-based social graphs. The drawback associated with the dependencies between layers and the order of node neighbourhood for the GCN can be more prevalent for friendship-based graphs. The evaluation of the full potential of the GCN on friendship-based social network requires openly available datasets in larger quantities. However, most available social network datasets are not complete. Also, the majority of the available social network datasets do not contain both the features and ground truth labels. In this work, firstly, we provide a guideline on simulating dynamic social networks, with ground truth labels and features, both coupled with the topology. Secondly, we introduce an open-source Python-based simulation library. We argue that the topology of the network is driven by a set of latent variables, termed as the social DNA (sDNA). We consider the sDNA as labels for the nodes. Finally, by evaluating on our simulated datasets, we propose four new variants of the GCN, mainly to overcome the limitation of dependency between the order of node-neighbourhood and a particular layer of the model. We then evaluate the performance of all the models and our results show that on 27 out of the 30 simulated datasets our proposed GCN variants outperform the original model.
A straightforward way to simulate graphs is to generate them using well-established network models @cite_12 : (1) Barab ' a si-Albert model for the scale-free network @cite_8 , (2) Watts-Strogatz small-world model for the small-world network @cite_34 , (3) Erd o s-R ' e nyi model for the random graph network @cite_38 @cite_3 @cite_41 @cite_33 , (4) Forest-fire Model model @cite_13 @cite_7 .
@cite_38 @cite_33 @cite_7 @cite_8 @cite_41 @cite_3 @cite_34 @cite_13 @cite_12
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The weak connectivity γ of a random net is defined and computed by an approximation method as a function ofa, the axone density. It is shown that γ rises rapidly witha, attaining 0.8 of its asymptotic value (unity) fora=2, where the number of neurons in the net is arbitrarily large. The significance of this parameter is interpreted also in terms of the maximum expected spread of an epidemic under certain conditions. If G is an arbitrary non-complete graph, let cZ1(G) denote the least number k such that by deleting k appropriately chosen vertices from G (i. e. deleting the k points in question and all edges starting from these points) the resulting graph is not connected. If G is a complete graph of order n, we put c,(G) = n-l. Let cY(G) denote the least number 1 such that by deleting 1 appropriately chosen edges from G the resulting graph is not connected. We may measure the strength of connectedness of G by any of the numbers c],(G), c$,(G) and in a certain sense if G is known to be connected) also by c(G). Evidently one has Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems. Networks of coupled dynamical systems have been used to model biological oscillators1,2,3,4, Josephson junction arrays5,6, excitable media7, neural networks8,9,10, spatial games11, genetic control networks12 and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them ‘small-world’ networks, by analogy with the small-world phenomenon13,14 (popularly known as six degrees of separation15). The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices. How do real graphs evolve over time? What are "normal" growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time.Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing super-linearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) or O(log(log n)).Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a "forest fire" spreading process, that has a simple, intuitive justification, requires very few parameters (like the "flammability" of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. Abstract Networks are everywhere and their many types, including social networks, the Internet, food webs etc., have been studied for the last few decades. However, in real-world networks, it’s hard to find examples that can be easily comparable, i.e. have the same density or even number of nodes and edges. We propose a flexible and extensible NetSim framework to understand how properties in different types of networks change with varying number of edges and vertices. Our approach enables to simulate three classical network models (random, small-world and scale-free) with easily adjustable model parameters and network size. To be able to compare different networks, for a single experimental setup we kept the number of edges and vertices fixed across the models. To understand how they change depending on the number of nodes and edges we ran over 30,000 simulations and analysed different network characteristics that cannot be derived analytically. Two of the main findings from the analysis are that the average shortest path does not change with the density of the scale-free network but changes for small-world and random networks; the apparent difference in mean betweenness centrality of the scale-free network compared with random and small-world networks.