String communityId = [Select Id from Network where Name = 'MobileMNOCS'].Id;

Integer depth = 3;

ConnectApi.ManagedTopicCollection managedTopic =

           ConnectApi.ManagedTopics.getManagedTopics(

                   communityId,ConnectApi.ManagedTopicType.Navigational,depth

               );

// you can set this map in constructor and can return this varible

Map<String, Map<String, List<String>>> pChildSubChildTopicsMap =

new Map<String, Map<String, List<String>>>();

Map<String, List<String>> childTopicsMap;

List<String> subChildTopicslist;

for(ConnectApi.ManagedTopic parentTopic : managedTopic.managedTopics){

	childTopicsMap = new Map<String, List<String>>();

	system.debug('Level1: ' + parentTopic.id + '    :    ' + parentTopic.Topic.Name);

	for(ConnectApi.ManagedTopic childTopic : parentTopic.children){

		subChildTopicslist = new List<String>();

		system.debug('Level2: ' + childTopic.id + '    :    ' + childTopic.Topic.Name);

		for(ConnectApi.ManagedTopic subChildTopic : childTopic.children){

		    //subChildTopicslist.add(subChildTopic.Topic.Name);

			system.debug('Level3: ' + subChildTopic.id + '    :    ' + subChildTopic.Topic.Name);

		}

		//childTopicsMap.put(childTopic.Topic.Name, subChildTopicslist);

	}

	//pChildSubChildTopicsMap.put(parentTopic.Topic.Name, childTopicsMap);

}