This is the IP address on router 4.4.4.4, the advertising router
With OSPF P2P links, you should see two links for each P2P adjacent router within the router LSA.
The first link is of link type P2P with a Link ID of the other router's router ID (2.2.2.2) and Link Data should be the IP address of the advertising router on the adjacent subnet (10.0.1.1)
You will also see a second link, which is a Stub Network link to the subnet on the adjacent interface. This will have a link ID of the network (not sure but could be 10.0.1.0 in this case) and Link Data will contain the subnet mask (255.255.255.0?)
This is all in the RFC 2328 page 129
This may seem confusing as you would expect the IP address to be that of the adjacent router. This information is not needed when calculating the SPF as OSPF only needs to see a connection to the other router and any onward networks reachable by that router. When the router needs to actually forward a packet to an adjacent router it uses the neighbor IP address's associated MAC address to forward the packet onwards. This IP address can be seen using show ip ospf neighbor on a Cisco router.
Set this up in the lab:
R1:
interface GigabitEthernet0/0
ip address 10.0.1.1 255.255.255.252
ip ospf network point-to-point
router ospf 1
router-id 4.4.4.4
network 10.0.0.0 0.255.255.255 area 0
R2:
interface GigabitEthernet0/1
ip address 10.0.1.2 255.255.255.252
ip ospf network point-to-point
router ospf 1
router-id 2.2.2.2
network 10.0.0.0 0.255.255.255 area 0
R1#sh ip ospf data router self-originate
OSPF Router with ID (4.4.4.4) (Process ID 1)
Router Link States (Area 0)
LS age: 66
Options: (No TOS-capability, DC)
LS Type: Router Links
Link State ID: 4.4.4.4
Advertising Router: 4.4.4.4
LS Seq Number: 80000004
Checksum: 0x865D
Length: 48
Number of Links: 2
Link connected to: another Router (point-to-point)
(Link ID) Neighboring Router ID: 2.2.2.2
(Link Data) Router Interface address: 10.0.1.1
Number of MTID metrics: 0
TOS 0 Metrics: 1
Link connected to: a Stub Network
(Link ID) Network/subnet number: 10.0.1.0
(Link Data) Network Mask: 255.255.255.252
Number of MTID metrics: 0
TOS 0 Metrics: 1
R2#sh ip ospf data router self-originate
OSPF Router with ID (2.2.2.2) (Process ID 1)
Router Link States (Area 0)
LS age: 105
Options: (No TOS-capability, DC)
LS Type: Router Links
Link State ID: 2.2.2.2
Advertising Router: 2.2.2.2
LS Seq Number: 80000004
Checksum: 0x7179
Length: 48
Number of Links: 2
Link connected to: another Router (point-to-point)
(Link ID) Neighboring Router ID: 4.4.4.4
(Link Data) Router Interface address: 10.0.1.2
Number of MTID metrics: 0
TOS 0 Metrics: 1
Link connected to: a Stub Network
(Link ID) Network/subnet number: 10.0.1.0
(Link Data) Network Mask: 255.255.255.252
Number of MTID metrics: 0
TOS 0 Metrics: 1