The average geodesic distance L Newman (2003) and the compactness CB Botafogo (1992) are important graph indices in applications of complex network theory to real-world problems. Here, for simple ...connected undirected graphs G of order n, we study the behavior of L(G) and CB(G), subject to the condition that their order |V(G)| approaches infinity. We prove that the limit of L(G)/n and CB(G) lies within the interval 0;1/3 and 2/3;1, respectively. Moreover, for any not necessarily rational number β ∈ 0;1/3 (α ∈ 2/3;1) we show how to construct the sequence of graphs {G}, |V(G)| = n → ∞, for which the limit of L(G)/n (CB(G)) is exactly β (α) (Theorems 1 and 2). Based on these results, our work points to novel classification possibilities of graphs at the node level as well as to the information-theoretic classification of the structural complexity of graph indices.
In this paper, we study the limit of compactness which is a graph index originally introduced for measuring structural characteristics of hypermedia. Applying compactness to large scale small-world ...graphs (Mehler, 2008) observed its limit behaviour to be equal 1. The striking question concerning this finding was whether this limit behaviour resulted from the specifics of small-world graphs or was simply an artefact. In this paper, we determine the necessary and sufficient conditions for any sequence of connected graphs resulting in a limit value of CB = 1 which can be generalized with some consideration for the case of disconnected graph classes (Theorem 3). This result can be applied to many well-known classes of connected graphs. Here, we illustrate it by considering four examples. In fact, our proof-theoretical approach allows for quickly obtaining the limit value of compactness for many graph classes sparing computational costs.
This article presents an approach to automatic language classification by means of linguistic networks. Networks of 11 languages were constructed from dependency treebanks, and the topology of these ...networks serves as input to the classification algorithm. The results match the genealogical similarities of these languages. In addition, we test two alternative approaches to automatic language classification - one based on n-grams and the other on quantitative typological indices. All three methods show good results in identifying genealogical groups. Beyond genetic similarities, network features (and feature combinations) offer a new source of typological information about languages. This information can contribute to a better understanding of the interplay of single linguistic phenomena observed in language.
The average geodesic distance L Newman (2003) and the compactness C.sub.B Botafogo (1992) are important graph indices in applications of complex network theory to real-world problems. Here, for ...simple connected undirected graphs G of order n, we study the behavior of L(G) and C.sub.B (G), subject to the condition that their order |V(G)| approaches infinity. We prove that the limit of L(G)/n and C.sub.B (G) lies within the interval 0;1/3 and 2/3;1, respectively. Moreover, for any not necessarily rational number beta element of 0;1/3 (alpha element of 2/3;1) we show how to construct the sequence of graphs {G}, |V(G)| = n right arrow infinity, for which the limit of L(G)/n (C.sub.B (G)) is exactly beta (alpha) (Theorems 1 and 2). Based on these results, our work points to novel classification possibilities of graphs at the node level as well as to the information-theoretic classification of the structural complexity of graph indices.
When young children learn to use language, they start to use their hands in co‐verbal gesturing. There are, however, considerable differences between children, and it is not completely understood ...what these individual differences are due to. We studied how children at 4 years of age employ speech and iconic gestures to convey meaning in different kinds of spatial event descriptions, and how this relates to their cognitive abilities. Focusing on spontaneous illustrations of actions, we applied a semantic feature (SF) analysis to characterize combinations of speech and gesture meaning and related them to the child's visual‐spatial abilities or /concrete reasoning abilities (measured using the standardized SON‐R 212−7 test). Results show that children with higher cognitive abilities convey significantly more meaning via gesture and less solely via speech. These findings suggest that young children's use of cospeech representational gesturing is positively related to their mental representation and reasoning abilities.
Based on the linguistic analysis of game explanations and retellings, the paper's goal is to investigate the relation of preschool children's situated discourse competence and iconic gestures in ...different communicative genres, focussing on reinforcing and supplementary speech-gesture-combinations. To this end, a method was developed to evaluate discourse competence as a context-sensitive and interactively embedded phenomenon. The so-called GLOBE-model was adapted to assess discourse competence in relation to interactive scaffolding. The findings show clear links between the children's competence and their parents' scaffolding. We suggest this to be evidence of a fine-tuned interactive support system. The results also indicate strong relations between higher discourse competence and increased frequency of iconic gestures. This applies in particular to reinforcing gestures. The results are interpreted as a confirmation that the speech-gesture system undergoes systematic changes during early childhood, and that gesturing becomes more iconic - and thus more communicative - when discourse competence is growing.
The average geodesic distance L Newman (2003) and the compactness CB Botafogo (1992) are important graph indices in applications of complex network theory to real-world problems. Here, for simple ...connected undirected graphs G of order n, we study the behavior of L(G) and CB(G), subject to the condition that their order |V(G)| approaches infinity. We prove that the limit of L(G)/n and CB(G) lies within the interval 0;1/3 and 2/3;1, respectively. Moreover, for any not necessarily rational number β ∈ 0;1/3 (α ∈ 2/3;1) we show how to construct the sequence of graphs {G}, |V(G)| = n → ∞, for which the limit of L(G)/n (CB(G)) is exactly β (α) (Theorems 1 and 2). Based on these results, our work points to novel classification possibilities of graphs at the node level as well as to the information-theoretic classification of the structural complexity of graph indices.
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