Matches in SemOpenAlex for { <https://semopenalex.org/work/W2256948834> ?p ?o ?g. }
Showing items 1 to 84 of
84
with 100 items per page.
- W2256948834 abstract "The following random graph model was introduced for the evolution of protein-protein interaction networks: Let $mathcal G = (G_n)_{n=n_0, n_0+1,...}$ be a sequence of random graphs, where $G_n = (V_n, E_n)$ is a graph with $|V_n|=n$ vertices, $n=n_0,n_0+1,...$ In state $G_n = (V_n, E_n)$, a vertex $vin V_n$ is chosen from $V_n$ uniformly at random and is partially duplicated. Upon such an event, a new vertex $v'notin V_n$ is created and every edge ${v,w} in E_n$ is copied with probability~$p$, i.e. $E_{n+1}$ has an edge ${v',w}$ with probability~$p$, independently of all other edges. Within this graph, we study several aspects for large~$n$. (i) The frequency of isolated vertices converges to~1 if $pleq p^* approx 0.567143$, the unique solution of $pe^p=1$. (ii) The number $C_k$ of $k$-cliques behaves like $n^{kp^{k-1}}$ in the sense that $n^{-kp^{k-1}}C_k$ converges against a non-trivial limit, if the starting graph has at least one $k$-clique. In particular, the average degree of a vertex (which equals the number of edges -- or 2-cliques -- divided by the size of the graph) converges to $0$ iff $p<0.5$ and we obtain that the transitivity ratio of the random graph is of the order $n^{-2p(1-p)}$. (iii) The evolution of the degrees of the vertices in the initial graph can be described explicitly. Here, we obtain the full distribution as well as convergence results." @default.
- W2256948834 created "2016-06-24" @default.
- W2256948834 creator A5044563257 @default.
- W2256948834 creator A5091710048 @default.
- W2256948834 date "2014-08-05" @default.
- W2256948834 modified "2023-09-27" @default.
- W2256948834 title "Large-scale behavior of the partial duplication random graph" @default.
- W2256948834 cites W1526841711 @default.
- W2256948834 cites W1588578190 @default.
- W2256948834 cites W160364443 @default.
- W2256948834 cites W17078302 @default.
- W2256948834 cites W1811172515 @default.
- W2256948834 cites W1873594873 @default.
- W2256948834 cites W1984137208 @default.
- W2256948834 cites W1989921625 @default.
- W2256948834 cites W2057693235 @default.
- W2256948834 cites W2063639254 @default.
- W2256948834 cites W2088048878 @default.
- W2256948834 cites W2106589950 @default.
- W2256948834 cites W2124637492 @default.
- W2256948834 cites W2126794261 @default.
- W2256948834 cites W2135123683 @default.
- W2256948834 cites W2139141215 @default.
- W2256948834 cites W2140827816 @default.
- W2256948834 cites W2143706916 @default.
- W2256948834 cites W2167680767 @default.
- W2256948834 cites W2169526870 @default.
- W2256948834 cites W2170201775 @default.
- W2256948834 cites W2170840812 @default.
- W2256948834 cites W2290127356 @default.
- W2256948834 cites W2801179766 @default.
- W2256948834 cites W2905110430 @default.
- W2256948834 cites W2964044865 @default.
- W2256948834 cites W91439453 @default.
- W2256948834 hasPublicationYear "2014" @default.
- W2256948834 type Work @default.
- W2256948834 sameAs 2256948834 @default.
- W2256948834 citedByCount "2" @default.
- W2256948834 countsByYear W22569488342014 @default.
- W2256948834 countsByYear W22569488342015 @default.
- W2256948834 crossrefType "posted-content" @default.
- W2256948834 hasAuthorship W2256948834A5044563257 @default.
- W2256948834 hasAuthorship W2256948834A5091710048 @default.
- W2256948834 hasConcept C114614502 @default.
- W2256948834 hasConcept C118615104 @default.
- W2256948834 hasConcept C132525143 @default.
- W2256948834 hasConcept C2985491264 @default.
- W2256948834 hasConcept C33923547 @default.
- W2256948834 hasConcept C47458327 @default.
- W2256948834 hasConcept C80899671 @default.
- W2256948834 hasConceptScore W2256948834C114614502 @default.
- W2256948834 hasConceptScore W2256948834C118615104 @default.
- W2256948834 hasConceptScore W2256948834C132525143 @default.
- W2256948834 hasConceptScore W2256948834C2985491264 @default.
- W2256948834 hasConceptScore W2256948834C33923547 @default.
- W2256948834 hasConceptScore W2256948834C47458327 @default.
- W2256948834 hasConceptScore W2256948834C80899671 @default.
- W2256948834 hasLocation W22569488341 @default.
- W2256948834 hasOpenAccess W2256948834 @default.
- W2256948834 hasPrimaryLocation W22569488341 @default.
- W2256948834 hasRelatedWork W105105908 @default.
- W2256948834 hasRelatedWork W1767936884 @default.
- W2256948834 hasRelatedWork W1902987962 @default.
- W2256948834 hasRelatedWork W2069505580 @default.
- W2256948834 hasRelatedWork W2125314709 @default.
- W2256948834 hasRelatedWork W2164172760 @default.
- W2256948834 hasRelatedWork W2260841063 @default.
- W2256948834 hasRelatedWork W2811223855 @default.
- W2256948834 hasRelatedWork W2899788998 @default.
- W2256948834 hasRelatedWork W2913713179 @default.
- W2256948834 hasRelatedWork W2931136162 @default.
- W2256948834 hasRelatedWork W2952049266 @default.
- W2256948834 hasRelatedWork W2963358149 @default.
- W2256948834 hasRelatedWork W2963404187 @default.
- W2256948834 hasRelatedWork W3015052924 @default.
- W2256948834 hasRelatedWork W3037745329 @default.
- W2256948834 hasRelatedWork W3113333471 @default.
- W2256948834 hasRelatedWork W3193803494 @default.
- W2256948834 hasRelatedWork W3197428793 @default.
- W2256948834 hasRelatedWork W3205558229 @default.
- W2256948834 isParatext "false" @default.
- W2256948834 isRetracted "false" @default.
- W2256948834 magId "2256948834" @default.
- W2256948834 workType "article" @default.