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.
Transitivity measured by the network clustering coefficient despite being extensively studied, is still one of the least understood properties in network analysis according to . Another important property we observe in real networks is the small-world effect -- all nodes are connected with each other by relatively short paths. To model these two properties Watts and Strogatz introduced a small-world network model @cite_34 .
@cite_34
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The small world phenomenon is a desirable property of social networks, since it guarantees short paths between the nodes of the social graph and thus efficient information spread on the network. It is thus in the benefit of both network users and network owners to enforce and maintain this property. In this work, we study the problem of finding a subset of k edges from a set of candidate edges whose addition to a network leads to the greatest reduction in its average shortest path length. We formulate the problem as a combinatorial optimization problem, and show that it is NP-hard and that known approximation techniques are not applicable. We describe an efficient method for computing the exact effect of a single edge insertion on the average shortest path length, as well as several heuristics for efficiently estimating this effect. We perform experiments on real data to study the performance of our algorithms in practice. In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the cross-over from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Pade approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the model. Appears in Phys. Rev. E 60, 7332-7342 (1999). A document is represented by a network; the nodes represent terms, and the edges represent the co-occurrence of terms. This paper shows that the network has the characteristics of being small world, i.e., highly clustered and short path length. Based on the topology, we can extract important terms, even if they are rare, by measuring their contribution to the graph being small world. In this article, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called random Apollonian networks (RANs) as they can be considered as a variation of Apollonian networks. We obtain the analytic results of power-law exponent gamma =3 and clustering coefficient C=(46 3)-36 ln (3 2) approx_equal 0.74, which agree with the simulation results very well. We prove that the increasing tendency of average distance of RANs is a little slower than the logarithm of the number of nodes in RANs. Since most real-life networks are both scale-free and small-world networks, RANs may perform well in mimicking the reality. The RANs possess hierarchical structure as C(k) approx k sup -1 that are in accord with the observations of many real-life networks. In addition, we prove that RANs are maximal planar networks, which are of particular practicability for layout of printed circuits and so on. The percolation and epidemic spreading process are also studied and the comparisons between RANs and Barabasi-Albert (BA) as well as Newman-Watts (NW) networks are shown. We find that, when the network order N (the total number of nodes) is relatively small (as N approx 10 sup 4 ), the performance of RANs under intentional attackmore » is not sensitive to N, while that of BA networks is much affected by N. And the diseases spread slower in RANs than BA networks in the early stage of the suseptible-infected process, indicating that the large clustering coefficient may slow the spreading velocity, especially in the outbreaks.« less