The non-violence of love:a Hildebrand-Girard encounter

If love is a social as well as a personal reality, it could be fruitful to compare Von Hildebrand’s understanding of love and desire with that of cultural anthropologist René Girard. Girard depicts love and desire as a triangular process which arises from imitation, rather than the result of auto-generative affection. In this sense, Girardian theory would seem to convict Von Hildebrand of what is called the romantic lie wherein desire is thought to arise through the mutual appreciation of two subjects. However, in The Nature of Love Von Hildebrand shows his awareness of the possibility that love can be awakened by imitation. Moreover, the lack of a sufficient reason in Girardian theory for avoiding violence can be answered by turning to Von Hildebrand’s appreciation of the ontological basis for desire.

Edge centrality via the Holevo quantity

In the study of complex networks, vertex centrality measures are used to identify the most important vertices within a graph. A related problem is that of measuring the centrality of an edge. In this paper, we propose a novel edge centrality index rooted in quantum information. More specifically, we measure the importance of an edge in terms of the contribution that it gives to the Von Neumann entropy of the graph. We show that this can be computed in terms of the Holevo quantity, a well known quantum information theoretical measure. While computing the Von Neumann entropy and hence the Holevo quantity requires computing the spectrum of the graph Laplacian, we show how to obtain a simplified measure through a quadratic approximation of the Shannon entropy. This in turns shows that the proposed centrality measure is strongly correlated with the negative degree centrality on the line graph. We evaluate our centrality measure through an extensive set of experiments on real-world as well as synthetic networks, and we compare it against commonly used alternative measures.