A Model of Directed Graph Cofiber

In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. This property does not apply when we discretize spaces and continuous maps to directed graphs and their morphisms. In this paper, we give a construction of a cofiber of a directed graph map whose image is contractible in the cofiber. Our work reveals that a category-theoretically correct construction in continuous setup is no longer correct when it is discretized and hence leads to look at canonical constructions in category theory in a different perspective.

Analysis of Regular Patterns in Un-weighted Directed Graphs

Time evolving networks tend to have an element of regularity. This regularity is characterized by existence of repetitive patterns in the data sequences of the graph metrics. As per our research, the relevance of such regular patterns to the network has not been adequately explored. Such patterns in certain data sequences are indicative of properties like popularity, activeness etc. which are of vital significance for any network. These properties are closely indicated by data sequences of graph metrics - degree prestige, degree centrality and occurrence. In this paper, (a) an improved mining algorithm has been used to extract regular patterns in these sequences, and (b) a methodology has been proposed to quantitatively analyse the behavior of the obtained patterns. To analyze this behavior, a quantification measure coined as "Sumscore" has been defined to compare the relative significance of such patterns. The patterns are ranked according to their Sumscores and insights are then drawn upon it. The efficacy of this method is demonstrated by experiments on two real world datasets.