Abstract
This paper describes modeling of social networks subject to recommendation. Cold Start User-Item Model (CSUIM) of bipartite graph is considered, which simulates bipartite graph growth based on several parameters. An algorithm is proposed to compute parameters of this model from real graph data so that real graph and its model have similar graph metrics.
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Notes
- 1.
The radius r of a graph is the minimum eccentricity of any vertex, \(r = \min _{v \in W} \epsilon (v)\). The eccentricity \(\epsilon (v)\) of a vertex v is the greatest geodesic distance between v and any other vertex.
- 2.
In bipartite graph for all vertices a, b in the same modality set we do not have any edges between them, so Local Clustering Coefficient (LCC) is always zero. Therefore, in [3] another suitable metric for clustering tendency was proposed — Bipartite Local Clustering Coefficient (BLCC). BLCC is defined as \(BLCC(u) = 1 -\frac{|N_2(u)|}{\sum _{v \in N_1(u)} (k_v- 1)}\), where W denote set of all vertices. Then \(N_s(n)\) is set of neighbours of vertex \(n \in W\), which are \(s \ge 1\) steps away. In other words \(N_s(n) = \{a \in W : K(n, a) = s\}\), where K(i, j) is minimal distance (number of edges) between vertices i and j. In [3] it is shown that graph metric LCC and BLCC are similar in classical graphs.
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Kłopotek, R.A. (2019). Modeling Bimodal Social Networks Subject to Recommendation. In: Damaševičius, R., Vasiljevienė, G. (eds) Information and Software Technologies. ICIST 2019. Communications in Computer and Information Science, vol 1078. Springer, Cham. https://doi.org/10.1007/978-3-030-30275-7_10
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