Hello Jaighobahi,
within a single OSPF area every router is able to draw the complete network topology using the information in the LS database.
The local node does not use only the LSA header, but actually the content of each LSA that is in the database.
For a single area OSPF domain the complete topology can be built by examining all the LSA type 1 and LSA type 2.
LSA type 1 are the Router LSA. Each router that has at least one interface in the area builds its own Router LSA and floods it in the area (area scope). The Router LSA has Link-id = OSPF router-id of advertising router and has entries describing all the links in the area.
Actually the links can be of different type : stub ( no OSPF neighbors) , point to point ( single OSPF neighbor), transit ( a LAN interface with potentially multiple neighbors).
The format of the link information changes for each link type. However, the key information is the following:
for point to point links the OSPF router-id of the neighbor is listed allowing to point to the neighbor's Router LSA.
for transit link a pointer to OSPF DR IP address is placed, this allows to point to a Network LSA generated by the OSPF DR in the LAN segment.
The Network LSA type 2 describes a network segment using a Link-id of the DR interface IP address. The Network LSA is a list of OSPF Router-ids of all routers connected to the segment including the OSPF DR itself.
When executing the SPF the local node starts from its own router LSA as the root of the SPF and then starts to search for the Router LSAs of its own neighbors.
Combining the information of Router LSAs and Network LSAs the local node learns all about inter router links and is able to say what routers are connected to a remote LAN segment in the same OSPF area.
Edit:
the picture you have linked is a graphical representation of the SPF algorithm and you can see it as the result of linking the Router LSA objects together with the help of the Network LSAs. The OSPF cost is that of the outgoing interface to reach the neighbor. So from a maths point of view the graph is oriented, different choices can be done in different directions as the cost might be different on the two ends of a link.
For LAN segment the cost is calculated as the cost to enter the LAN.
Then for each IPv4 prefix within the area the SPF finds the shortest path = lowest total cost from the point of view of the local node.
As you see the link state nature of OSPF allows for this.
In OSPF multi area other types of OSPF LSAs are used, but the link state nature is limited to a single area. The information coming from other areas does not contain topological information.
Hope to help
Giuseppe
