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I am looking for an application that allows to display a dependency graph, and the "entities" that are part of the graph.
Suppose I define the "task" entity; the software should allow me to define the fields associated to that entity, which include a reference to other tasks. It should then show the entities in a graph that evidences which task have a dependency, and with what. In that way, I could pick up a task without dependencies, or the task from which three or more other tasks depends from.

Differently from a Gantt chart, time is not involved in the graph I am referring. The application should be generic enough to work with any entities, and any data associated with them; in my example, I could be able to replace task with project, person, company.

Is there such an application? What is the application that is closer to the requirements I reported?

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If you are willing to write the code that traverses the dependency graph, there are a large number of applications that will display it. The easiest start would be to look at digraphs in GraphViz. graphviz.org I've used JGrapht in Java, Groovy, and other JVM languages, and Mathematica as well, if those are options for you. –  Art Taylor Sep 26 '11 at 5:25
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