Question: How are graphs derived from a given text?
Evidence: In this work we consider directed graphs. Let INLINEFORM0 represent a graph comprised of a set of vertices INLINEFORM1 and a set of edges ( INLINEFORM2 ), which are ordered pairs. Further, each edge can have a real-valued weight assigned. Let INLINEFORM3 represent a document comprised of tokens INLINEFORM4 . The order in which tokens in text appear is known, thus INLINEFORM5 is a totally ordered set. A potential way of constructing a graph from a document is by simply observing word co-occurrences. When two words co-occur, they are used as an edge. However, such approaches do not take into account the sequence nature of the words, meaning that the order is lost. We attempt to take this aspect into account as follows. The given corpus is traversed, and for each element INLINEFORM6 , its successor INLINEFORM7 , together with a given element, forms a directed edge INLINEFORM8 . Finally, such edges are weighted according to the number of times they appear in a given corpus. Thus the graph, constructed after traversing a given corpus, consists of all local neighborhoods (order one), merged into a single joint structure. Global contextual information is potentially kept intact (via weights), even though it needs to be detected via network analysis as proposed next.
In this work we consider directed graphs. Let INLINEFORM0 represent a graph comprised of a set of vertices INLINEFORM1 and a set of edges ( INLINEFORM2 ), which are ordered pairs. Further, each edge can have a real-valued weight assigned. Let INLINEFORM3 represent a document comprised of tokens INLINEFORM4 . The order in which tokens in text appear is known, thus INLINEFORM5 is a totally ordered set. A potential way of constructing a graph from a document is by simply observing word co-occurrences. When two words co-occur, they are used as an edge. However, such approaches do not take into account the sequence nature of the words, meaning that the order is lost. We attempt to take this aspect into account as follows. The given corpus is traversed, and for each element INLINEFORM6 , its successor INLINEFORM7 , together with a given element, forms a directed edge INLINEFORM8 . Finally, such edges are weighted according to the number of times they appear in a given corpus. Thus the graph, constructed after traversing a given corpus, consists of all local neighborhoods (order one), merged into a single joint structure. Global contextual information is potentially kept intact (via weights), even though it needs to be detected via network analysis as proposed next.
Answer: The answers are shown as follows:
* The given corpus is traversed, and for each element INLINEFORM6 , its successor INLINEFORM7 , together with a given element, forms a directed edge INLINEFORM8 . Finally, such edges are weighted according to the number of times they appear in a given corpus. Thus the graph, constructed after traversing a given corpus, consists of all local neighborhoods (order one), merged into a single joint structure. Global contextual information is potentially kept intact (via weights), even though it needs to be detected via network analysis