我的工作环境：
mongo-1:"172.28.32.58:28010"
mongo-2:"172.28.32.59:28010"
mongo-3:"172.28.32.60:28010"

NOTE: filename: test_pymongo.py

from pymongo import MongoClient
from pymongo import ReadPreference

# single mongo
#c = MongoClient(host="mongo-1", port=28010) # okay
#c = MongoClient('mongodb://admin:123456@mongo-1:28010,mongo-2:28010/?replicaSet=rsname')

# mongo cluster
#c = MongoClient('mongodb://admin:123456@mongo-1:28010,mongo-2:28010,mongo-3:28010')
c = MongoClient('mongodb://admin:123456@mongo-1:28010,mongo-2:28010,mongo-3:28010',read_preference=ReadPreference.SECONDARY)
c = MongoClient('mongodb://admin:123456@mongo-1:28010,mongo-2:28010,mongo-3:28010',read_preference=ReadPreference. SECONDARY_PREFERRED)
#c = MongoClient('mongodb://admin:123456@mongo-1:28010,mongo-2:28010,mongo-3:28010',read_preference=ReadPreference.NEAREST)
#c = MongoClient('mongodb://admin:123456@mongo-1:28010,mongo-2:28010,mongo-3:28010/?readPreference=secondary')
#c = MongoClient('mongodb://admin:123456@mongo-3:28010/?readPreference=secondary')

print c.nodes
print c.database_names()

输出结果：

$ python test_pymongo.py
Traceback (most recent call last):
  File "test_pymongo.py", line 16, in <module>
    print c.database_names()
  File "/root/.virtualenvs/py2.7.13mpc/lib/python2.7/site-packages/pymongo/mongo_client.py", line 1088, in database_names
    "listDatabases")["databases"]]
  File "/root/.virtualenvs/py2.7.13mpc/lib/python2.7/site-packages/pymongo/database.py", line 478, in command
    with client._socket_for_reads(read_preference) as (sock_info, slave_ok):
  File "/root/.pyenv/versions/2.7.13/lib/python2.7/contextlib.py", line 17, in __enter__
    return self.gen.next()
  File "/root/.virtualenvs/py2.7.13mpc/lib/python2.7/site-packages/pymongo/mongo_client.py", line 798, in _socket_for_reads
    with self._get_socket(read_preference) as sock_info:
  File "/root/.pyenv/versions/2.7.13/lib/python2.7/contextlib.py", line 17, in __enter__
    return self.gen.next()
  File "/root/.virtualenvs/py2.7.13mpc/lib/python2.7/site-packages/pymongo/mongo_client.py", line 762, in _get_socket
    server = self._get_topology().select_server(selector)
  File "/root/.virtualenvs/py2.7.13mpc/lib/python2.7/site-packages/pymongo/topology.py", line 210, in select_server
    address))
  File "/root/.virtualenvs/py2.7.13mpc/lib/python2.7/site-packages/pymongo/topology.py", line 186, in select_servers
    self._error_message(selector))
pymongo.errors.ServerSelectionTimeoutError: No replica set members match selector "Primary()"

连接到mongo-2:

$ /opt/mongodb/bin/mongo 127.0.0.1:28010
MongoDB shell version: 3.2.12
connecting to: 127.0.0.1:28010/test
sys95:PRIMARY> use admin;
switched to db admin
sys95:PRIMARY> db.auth('admin','123456')
1
sys95:SECONDARY> rs.slaveOk();
sys95:SECONDARY> show dbs;
admin  0.000GB
cmdb   0.001GB
local  0.002GB
mpc    0.001GB
uop    0.000GB

sys95:SECONDARY> rs.conf();
{
    "_id" : "sys95",
    "version" : 1,
    "protocolVersion" : NumberLong(1),
    "members" : [
        {
            "_id" : 0,
            "host" : "172.28.32.58:28010",
            "arbiterOnly" : false,
            "buildIndexes" : true,
            "hidden" : false,
            "priority" : 3,
            "tags" : {

            },
            "slaveDelay" : NumberLong(0),
            "votes" : 1
        },
        {
            "_id" : 1,
            "host" : "172.28.32.59:28010",
            "arbiterOnly" : false,
            "buildIndexes" : true,
            "hidden" : false,
            "priority" : 2,
            "tags" : {

            },
            "slaveDelay" : NumberLong(0),
            "votes" : 1
        },
        {
            "_id" : 2,
            "host" : "172.28.32.60:28010",
            "arbiterOnly" : false,
            "buildIndexes" : true,
            "hidden" : false,
            "priority" : 1,
            "tags" : {

            },
            "slaveDelay" : NumberLong(0),
            "votes" : 1
        }
    ],
    "settings" : {
        "chainingAllowed" : true,
        "heartbeatIntervalMillis" : 2000,
        "heartbeatTimeoutSecs" : 10,
        "electionTimeoutMillis" : 10000,
        "getLastErrorModes" : {

        },
        "getLastErrorDefaults" : {
            "w" : 1,
            "wtimeout" : 0
        },
        "replicaSetId" : ObjectId("597955a8d6042b84ccda4599")
    }
}
sys95:SECONDARY>

sys95:SECONDARY> rs.status();
{
    "set" : "sys95",
    "date" : ISODate("2017-08-10T13:54:20.760Z"),
    "myState" : 2,
    "term" : NumberLong(13),
    "heartbeatIntervalMillis" : NumberLong(2000),
    "members" : [
        {
            "_id" : 0,
            "name" : "172.28.32.58:28010",
            "health" : 0,
            "state" : 8,
            "stateStr" : "(not reachable/healthy)",
            "uptime" : 0,
            "optime" : {
                "ts" : Timestamp(0, 0),
                "t" : NumberLong(-1)
            },
            "optimeDate" : ISODate("1970-01-01T00:00:00Z"),
            "lastHeartbeat" : ISODate("2017-08-10T13:54:14.845Z"),
            "lastHeartbeatRecv" : ISODate("2017-08-10T13:31:34.288Z"),
            "pingMs" : NumberLong(0),
            "lastHeartbeatMessage" : "No route to host",
            "configVersion" : -1
        },
        {
            "_id" : 1,
            "name" : "172.28.32.59:28010",
            "health" : 1,
            "state" : 2,
            "stateStr" : "SECONDARY",  ## mongo-2 is work well!
            "uptime" : 8331,
            "optime" : {
                "ts" : Timestamp(1502371925, 1),
                "t" : NumberLong(13)
            },
            "optimeDate" : ISODate("2017-08-10T13:32:05Z"),
            "infoMessage" : "could not find member to sync from",
            "configVersion" : 1,
            "self" : true
        },
        {
            "_id" : 2,
            "name" : "172.28.32.60:28010",
            "health" : 0,
            "state" : 8,
            "stateStr" : "(not reachable/healthy)",
            "uptime" : 0,
            "optime" : {
                "ts" : Timestamp(0, 0),
                "t" : NumberLong(-1)
            },
            "optimeDate" : ISODate("1970-01-01T00:00:00Z"),
            "lastHeartbeat" : ISODate("2017-08-10T13:54:16.797Z"),
            "lastHeartbeatRecv" : ISODate("2017-08-10T13:32:10.636Z"),
            "pingMs" : NumberLong(0),
            "lastHeartbeatMessage" : "No route to host",
            "configVersion" : -1
        }
    ],
    "ok" : 1
}
sys95:SECONDARY>

sys95:SECONDARY> rs.isMaster()
{
    "hosts" : [
        "172.28.32.58:28010",
        "172.28.32.59:28010",
        "172.28.32.60:28010"
    ],
    "setName" : "sys95",
    "setVersion" : 1,
    "ismaster" : false,
    "secondary" : true,
    "me" : "172.28.32.59:28010",
    "maxBsonObjectSize" : 16777216,
    "maxMessageSizeBytes" : 48000000,
    "maxWriteBatchSize" : 1000,
    "localTime" : ISODate("2017-08-11T02:39:19.300Z"),
    "maxWireVersion" : 4,
    "minWireVersion" : 0,
    "ok" : 1
}

结果：
和DBA确认过，如果Mongo集群中有3个节点，2个关掉之后，只保留一个secondary节点，没有primary节点，是无法对外提供功能的。

No primary available for writes

No replica set members match selector "Primary()"

扩展阅读：

High Availability and PyMongo¶
http://api.mongodb.com/python/current/examples/high_availability.html

简介：

Read preference:

Read preference is configured using one of the classes from read_preferences (Primary, PrimaryPreferred, Secondary, SecondaryPreferred, or Nearest). For convenience, we also provide ReadPreference with the following attributes:

PRIMARY: Read from the primary. This is the default read preference, and provides the strongest consistency. If no primary is available, raise AutoReconnect.
PRIMARY_PREFERRED: Read from the primary if available, otherwise read from a secondary.
SECONDARY: Read from a secondary. If no matching secondary is available, raise AutoReconnect.
SECONDARY_PREFERRED: Read from a secondary if available, otherwise from the primary.
NEAREST: Read from any available member.

https://stackoverflow.com/questions/38762897/pymongo-unable-to-connect-to-primary/45616549#45616549
简介：
stackoverfow 上一个类似的问题。

pymongo unable to connect to primary